# Function Reference

This appendix provides a list of all the functions which are currently defined in Gnumeric.

## Bitwise Operations

`BITAND`
`BITAND` bitwise and

    BITAND(a,b)

#### Arguments

a: non-negative integer

b: non-negative integer

#### Description

`BITAND` returns the bitwise and of the binary representations of its arguments.

#### See also

`BITOR`, `BITXOR`.

`BITLSHIFT`
`BITLSHIFT` bit-shift to the left

    BITLSHIFT(a,n)

#### Arguments

a: non-negative integer

n: integer

#### Description

`BITLSHIFT` returns the binary representations of a shifted n positions to the left.

#### Note

If n is negative, `BITLSHIFT` shifts the bits to the right by ABS(n) positions.

#### See also

`BITRSHIFT`.

`BITOR`
`BITOR` bitwise or

    BITOR(a,b)

#### Arguments

a: non-negative integer

b: non-negative integer

#### Description

`BITOR` returns the bitwise or of the binary representations of its arguments.

#### See also

`BITXOR`, `BITAND`.

`BITRSHIFT`
`BITRSHIFT` bit-shift to the right

    BITRSHIFT(a,n)

#### Arguments

a: non-negative integer

n: integer

#### Description

`BITRSHIFT` returns the binary representations of a shifted n positions to the right.

#### Note

If n is negative, `BITRSHIFT` shifts the bits to the left by ABS(n) positions.

#### See also

`BITLSHIFT`.

`BITXOR`
`BITXOR` bitwise exclusive or

    BITXOR(a,b)

#### Arguments

a: non-negative integer

b: non-negative integer

#### Description

`BITXOR` returns the bitwise exclusive or of the binary representations of its arguments.

#### See also

`BITOR`, `BITAND`.

## Complex

`COMPLEX`
`COMPLEX` a complex number of the form x + y i

    COMPLEX(x,y,i)

#### Arguments

x: real part

y: imaginary part

i: the suffix for the complex number, either "i" or "j"; defaults to "i"

#### Note

If i is neither "i" nor "j", `COMPLEX` returns #VALUE!

#### Microsoft Excel Compatibility

This function is Excel compatible.

`IMABS`
`IMABS` the absolute value of the complex number z

    IMABS(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMAGINARY`, `IMREAL`.

`IMAGINARY`
`IMAGINARY` the imaginary part of the complex number z

    IMAGINARY(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMREAL`.

`IMARCCOS`
`IMARCCOS` the complex arccosine of the complex number

    IMARCCOS(z)

#### Arguments

z: a complex number

#### Description

`IMARCCOS` returns the complex arccosine of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCSIN`, `IMARCTAN`.

`IMARCCOSH`
`IMARCCOSH` the complex hyperbolic arccosine of the complex number z

    IMARCCOSH(z)

#### Arguments

z: a complex number

#### Description

`IMARCCOSH` returns the complex hyperbolic arccosine of the complex number z. The branch cut is on the real axis, less than 1.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCSINH`, `IMARCTANH`.

`IMARCCOT`
`IMARCCOT` the complex arccotangent of the complex number z

    IMARCCOT(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCSEC`, `IMARCCSC`.

`IMARCCOTH`
`IMARCCOTH` the complex hyperbolic arccotangent of the complex number z

    IMARCCOTH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCSECH`, `IMARCCSCH`.

`IMARCCSC`
`IMARCCSC` the complex arccosecant of the complex number z

    IMARCCSC(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCSEC`, `IMARCCOT`.

`IMARCCSCH`
`IMARCCSCH` the complex hyperbolic arccosecant of the complex number z

    IMARCCSCH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCSECH`, `IMARCCOTH`.

`IMARCSEC`
`IMARCSEC` the complex arcsecant of the complex number z

    IMARCSEC(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCCSC`, `IMARCCOT`.

`IMARCSECH`
`IMARCSECH` the complex hyperbolic arcsecant of the complex number z

    IMARCSECH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCCSCH`, `IMARCCOTH`.

`IMARCSIN`
`IMARCSIN` the complex arcsine of the complex number z

    IMARCSIN(z)

#### Arguments

z: a complex number

#### Description

`IMARCSIN` returns the complex arcsine of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCCOS`, `IMARCTAN`.

`IMARCSINH`
`IMARCSINH` the complex hyperbolic arcsine of the complex number z

    IMARCSINH(z)

#### Arguments

z: a complex number

#### Description

`IMARCSINH` returns the complex hyperbolic arcsine of the complex number z. The branch cuts are on the imaginary axis, below -i and above i.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCCOSH`, `IMARCTANH`.

`IMARCTAN`
`IMARCTAN` the complex arctangent of the complex number

    IMARCTAN(z)

#### Arguments

z: a complex number

#### Description

`IMARCTAN` returns the complex arctangent of the complex number z. The branch cuts are on the imaginary axis, below -i and above i.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCSIN`, `IMARCCOS`.

`IMARCTANH`
`IMARCTANH` the complex hyperbolic arctangent of the complex number z

    IMARCTANH(z)

#### Arguments

z: a complex number

#### Description

`IMARCTANH` returns the complex hyperbolic arctangent of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMARCSINH`, `IMARCCOSH`.

`IMARGUMENT`
`IMARGUMENT` the argument theta of the complex number z

    IMARGUMENT(z)

#### Arguments

z: a complex number

#### Description

The argument theta of a complex number is its angle in radians from the real axis.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`IMCONJUGATE`
`IMCONJUGATE` the complex conjugate of the complex number z

    IMCONJUGATE(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMAGINARY`, `IMREAL`.

`IMCOS`
`IMCOS` the cosine of the complex number z

    IMCOS(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMSIN`, `IMTAN`.

`IMCOSH`
`IMCOSH` the hyperbolic cosine of the complex number z

    IMCOSH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMSINH`, `IMTANH`.

`IMCOT`
`IMCOT` the cotangent of the complex number z

    IMCOT(z)

#### Arguments

z: a complex number

#### Description

cotz = cosz/sinz.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMSEC`, `IMCSC`.

`IMCOTH`
`IMCOTH` the hyperbolic cotangent of the complex number z

    IMCOTH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMSECH`, `IMCSCH`.

`IMCSC`
`IMCSC` the cosecant of the complex number z

    IMCSC(z)

#### Arguments

z: a complex number

#### Description

cscz = 1/sinz.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMSEC`, `IMCOT`.

`IMCSCH`
`IMCSCH` the hyperbolic cosecant of the complex number z

    IMCSCH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMSECH`, `IMCOTH`.

`IMDIV`
`IMDIV` the quotient of two complex numbers z1/z2

    IMDIV(z1,z2)

#### Arguments

z1: a complex number

z2: a complex number

#### Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMPRODUCT`.

`IMEXP`
`IMEXP` the exponential of the complex number z

    IMEXP(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMLN`.

`IMINV`
`IMINV` the reciprocal, or inverse, of the complex number z

    IMINV(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

`IMLN`
`IMLN` the natural logarithm of the complex number z

    IMLN(z)

#### Arguments

z: a complex number

#### Description

The result will have an imaginary part between -π and +π.

The natural logarithm is not uniquely defined on complex numbers. You may need to add or subtract an even multiple of π to the imaginary part.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMEXP`, `IMLOG2`, `IMLOG10`.

`IMLOG10`
`IMLOG10` the base-10 logarithm of the complex number z

    IMLOG10(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMLN`, `IMLOG2`.

`IMLOG2`
`IMLOG2` the base-2 logarithm of the complex number z

    IMLOG2(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMLN`, `IMLOG10`.

`IMNEG`
`IMNEG` the negative of the complex number z

    IMNEG(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

`IMPOWER`
`IMPOWER` the complex number z1 raised to the z2th power

    IMPOWER(z1,z2)

#### Arguments

z1: a complex number

z2: a complex number

#### Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMSQRT`.

`IMPRODUCT`
`IMPRODUCT` the product of the given complex numbers

    IMPRODUCT(z1,z2)

#### Arguments

z1: a complex number

z2: a complex number

#### Note

If any of z1, z2,... is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMDIV`.

`IMREAL`
`IMREAL` the real part of the complex number z

    IMREAL(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMAGINARY`.

`IMSEC`
`IMSEC` the secant of the complex number z

    IMSEC(z)

#### Arguments

z: a complex number

#### Description

secz = 1/cosz.

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMCSC`, `IMCOT`.

`IMSECH`
`IMSECH` the hyperbolic secant of the complex number z

    IMSECH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMCSCH`, `IMCOTH`.

`IMSIN`
`IMSIN` the sine of the complex number z

    IMSIN(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMCOS`, `IMTAN`.

`IMSINH`
`IMSINH` the hyperbolic sine of the complex number z

    IMSINH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMCOSH`, `IMTANH`.

`IMSQRT`
`IMSQRT` the square root of the complex number z

    IMSQRT(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMPOWER`.

`IMSUB`
`IMSUB` the difference of two complex numbers

    IMSUB(z1,z2)

#### Arguments

z1: a complex number

z2: a complex number

#### Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMSUM`.

`IMSUM`
`IMSUM` the sum of the given complex numbers

    IMSUM(z1,z2)

#### Arguments

z1: a complex number

z2: a complex number

#### Note

If any of z1, z2,... is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMSUB`.

`IMTAN`
`IMTAN` the tangent of the complex number z

    IMTAN(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`IMSIN`, `IMCOS`.

`IMTANH`
`IMTANH` the hyperbolic tangent of the complex number z

    IMTANH(z)

#### Arguments

z: a complex number

#### Note

If z is not a valid complex number, #VALUE! is returned.

#### See also

`IMSINH`, `IMCOSH`.

## Database

`DAVERAGE`
`DAVERAGE` average of the values in field in database belonging to records that match criteria

    DAVERAGE(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DCOUNT`.

`DCOUNT`
`DCOUNT` count of numbers in field in database belonging to records that match criteria

    DCOUNT(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DAVERAGE`, `DCOUNTA`.

`DCOUNTA`
`DCOUNTA` count of cells with data in field in database belonging to records that match criteria

    DCOUNTA(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DCOUNT`.

`DGET`
`DGET` a value from field in database belonging to records that match criteria

    DGET(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### Note

If none of the records match the conditions, `DGET` returns #VALUE! If more than one record match the conditions, `DGET` returns #NUM!

#### See also

`DCOUNT`.

`DMAX`
`DMAX` largest number in field in database belonging to a record that match criteria

    DMAX(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DMIN`.

`DMIN`
`DMIN` smallest number in field in database belonging to a record that match criteria

    DMIN(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DCOUNT`.

`DPRODUCT`
`DPRODUCT` product of all values in field in database belonging to records that match criteria

    DPRODUCT(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DSUM`.

`DSTDEV`
`DSTDEV` sample standard deviation of the values in field in database belonging to records that match criteria

    DSTDEV(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DSTDEVP`.

`DSTDEVP`
`DSTDEVP` standard deviation of the population of values in field in database belonging to records that match criteria

    DSTDEVP(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DSTDEV`.

`DSUM`
`DSUM` sum of the values in field in database belonging to records that match criteria

    DSUM(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DPRODUCT`.

`DVAR`
`DVAR` sample variance of the values in field in database belonging to records that match criteria

    DVAR(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DVARP`.

`DVARP`
`DVARP` variance of the population of values in field in database belonging to records that match criteria

    DVARP(database,field,criteria)

#### Arguments

database: a range in which rows of related information are records and columns of data are fields

field: a string or integer specifying which field is to be used

criteria: a range containing conditions

#### Description

database is a range in which rows of related information are records and columns of data are fields. The first row of a database contains labels for each column.

field is a string or integer specifying which field is to be used. If field is an integer n then the nth column will be used. If field is a string, then the column with the matching label will be used.

criteria is a range containing conditions. The first row of a criteria should contain labels. Each label specifies to which field the conditions given in that column apply. Each cell below the label specifies a condition such as ">3" or "<9". An equality condition can be given by simply specifying a value, e. g. "3" or "Jody". For a record to be considered it must satisfy all conditions in at least one of the rows of criteria.

#### See also

`DVAR`.

`GETPIVOTDATA`
`GETPIVOTDATA` summary data from a pivot table

    GETPIVOTDATA(pivot_table,field_name)

#### Arguments

pivot_table: cell range containing the pivot table

field_name: name of the field for which the summary data is requested

#### Note

If the summary data is unavailable, `GETPIVOTDATA` returns #REF!

## Date/Time

`ASCENSIONTHURSDAY`
`ASCENSIONTHURSDAY` Ascension Thursday in the Gregorian calendar according to the Roman rite of the Christian Church

    ASCENSIONTHURSDAY(year)

#### Arguments

year: year between 1582 and 9956, defaults to the year of the next Ascension Thursday

#### Note

Two digit years are adjusted as elsewhere in Gnumeric. Dates before 1904 may also be prohibited.

#### See also

`EASTERSUNDAY`.

`ASHWEDNESDAY`
`ASHWEDNESDAY` Ash Wednesday in the Gregorian calendar according to the Roman rite of the Christian Church

    ASHWEDNESDAY(year)

#### Arguments

year: year between 1582 and 9956, defaults to the year of the next Ash Wednesday

#### Note

Two digit years are adjusted as elsewhere in Gnumeric. Dates before 1904 may also be prohibited.

#### See also

`EASTERSUNDAY`.

`DATE`
`DATE` create a date serial value

    DATE(year,month,day)

#### Arguments

year: year of date

month: month of year

day: day of month

#### Description

The `DATE` function creates date serial values. 1-Jan-1900 is serial value 1, 2-Jan-1900 is serial value 2, and so on. For compatibility reasons, a serial value is reserved for the non-existing date 29-Feb-1900.

#### Note

If month or day is less than 1 or too big, then the year and/or month will be adjusted. For spreadsheets created with the Mac version of Excel, serial 1 is 1-Jan-1904.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TODAY`, `YEAR`, `MONTH`, `DAY`.

`DATE2HDATE`
`DATE2HDATE` Hebrew date

    DATE2HDATE(date)

#### Arguments

date: Gregorian date, defaults to today

#### See also

`HDATE`, `DATE2HDATE_HEB`.

`DATE2HDATE_HEB`
`DATE2HDATE_HEB` Hebrew date in Hebrew

    DATE2HDATE_HEB(date)

#### Arguments

date: Gregorian date, defaults to today

#### See also

`DATE2HDATE`, `HDATE_HEB`.

`DATE2JULIAN`
`DATE2JULIAN` Julian day number for given Gregorian date

    DATE2JULIAN(date)

#### Arguments

date: Gregorian date, defaults to today

#### See also

`HDATE_JULIAN`.

`DATE2UNIX`
`DATE2UNIX` the Unix timestamp corresponding to a date d

    DATE2UNIX(d)

#### Arguments

d: date

#### Description

The `DATE2UNIX` function translates a date into a Unix timestamp. A Unix timestamp is the number of seconds since midnight (0:00) of January 1st, 1970 GMT.

#### See also

`UNIX2DATE`, `DATE`.

`DATEDIF`
`DATEDIF` difference between dates

    DATEDIF(start_date,end_date,interval)

#### Arguments

start_date: starting date serial value

end_date: ending date serial value

interval: counting unit

#### Description

`DATEDIF` returns the distance from start_date to end_date according to the unit specified by interval.

#### Note

If interval is "y", "m", or "d" then the distance is measured in complete years, months, or days respectively. If interval is "ym" or "yd" then the distance is measured in complete months or days, respectively, but excluding any difference in years. If interval is "md" then the distance is measured in complete days but excluding any difference in months.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DAYS360`.

`DATEVALUE`
`DATEVALUE` the date part of a date and time serial value

    DATEVALUE(serial)

#### Arguments

serial: date and time serial value

#### Description

`DATEVALUE` returns the date serial value part of a date and time serial value.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TIMEVALUE`, `DATE`.

`DAY`
`DAY` the day-of-month part of a date serial value

    DAY(date)

#### Arguments

date: date serial value

#### Description

The `DAY` function returns the day-of-month part of date.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATE`, `YEAR`, `MONTH`.

`DAYS`
`DAYS` difference between dates in days

    DAYS(start_date,end_date)

#### Arguments

start_date: starting date serial value

end_date: ending date serial value

#### Description

`DAYS` returns the positive or negative number of days from start_date to end_date.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`DATEDIF`.

`DAYS360`
`DAYS360` days between dates

    DAYS360(start_date,end_date,method)

#### Arguments

start_date: starting date serial value

end_date: ending date serial value

method: counting method

#### Description

`DAYS360` returns the number of days from start_date to end_date.

#### Note

If method is 0, the default, the MS Excel (tm) US method will be used. This is a somewhat complicated industry standard method where the last day of February is considered to be the 30th day of the month, but only for start_date. If method is 1, the European method will be used. In this case, if the day of the month is 31 it will be considered as 30 If method is 2, a saner version of the US method is used in which both dates get the same February treatment.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATEDIF`.

`EASTERSUNDAY`
`EASTERSUNDAY` Easter Sunday in the Gregorian calendar according to the Roman rite of the Christian Church

    EASTERSUNDAY(year)

#### Arguments

year: year between 1582 and 9956, defaults to the year of the next Easter Sunday

#### Note

Two digit years are adjusted as elsewhere in Gnumeric. Dates before 1904 may also be prohibited.

#### OpenDocument Format (ODF) Compatibility

The 1-argument version of `EASTERSUNDAY` is compatible with OpenOffice for years after 1904. This function is not specified in ODF/OpenFormula.

#### See also

`ASHWEDNESDAY`.

`EDATE`
`EDATE` adjust a date by a number of months

    EDATE(date,months)

#### Arguments

date: date serial value

months: signed number of months

#### Description

`EDATE` returns date moved forward or backward the number of months specified by months.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATE`.

`EOMONTH`
`EOMONTH` end of month

    EOMONTH(date,months)

#### Arguments

date: date serial value

months: signed number of months

#### Description

`EOMONTH` returns the date serial value of the end of the month specified by date adjusted forward or backward the number of months specified by months.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`EDATE`.

`GOODFRIDAY`
`GOODFRIDAY` Good Friday in the Gregorian calendar according to the Roman rite of the Christian Church

    GOODFRIDAY(year)

#### Arguments

year: year between 1582 and 9956, defaults to the year of the next Good Friday

#### Note

Two digit years are adjusted as elsewhere in Gnumeric. Dates before 1904 may also be prohibited.

#### See also

`EASTERSUNDAY`.

`HDATE`
`HDATE` Hebrew date

    HDATE(year,month,day)

#### Arguments

year: Gregorian year of date, defaults to the current year

month: Gregorian month of year, defaults to the current month

day: Gregorian day of month, defaults to the current day

#### See also

`HDATE_HEB`, `DATE`.

`HDATE_DAY`
`HDATE_DAY` Hebrew day of Gregorian date

    HDATE_DAY(year,month,day)

#### Arguments

year: Gregorian year of date, defaults to the current year

month: Gregorian month of year, defaults to the current month

day: Gregorian day of month, defaults to the current day

#### See also

`HDATE_JULIAN`.

`HDATE_HEB`
`HDATE_HEB` Hebrew date in Hebrew

    HDATE_HEB(year,month,day)

#### Arguments

year: Gregorian year of date, defaults to the current year

month: Gregorian month of year, defaults to the current month

day: Gregorian day of month, defaults to the current day

#### See also

`HDATE`, `DATE`.

`HDATE_JULIAN`
`HDATE_JULIAN` Julian day number for given Gregorian date

    HDATE_JULIAN(year,month,day)

#### Arguments

year: Gregorian year of date, defaults to the current year

month: Gregorian month of year, defaults to the current month

day: Gregorian day of month, defaults to the current day

#### See also

`HDATE`.

`HDATE_MONTH`
`HDATE_MONTH` Hebrew month of Gregorian date

    HDATE_MONTH(year,month,day)

#### Arguments

year: Gregorian year of date, defaults to the current year

month: Gregorian month of year, defaults to the current month

day: Gregorian day of month, defaults to the current day

#### See also

`HDATE_JULIAN`.

`HDATE_YEAR`
`HDATE_YEAR` Hebrew year of Gregorian date

    HDATE_YEAR(year,month,day)

#### Arguments

year: Gregorian year of date, defaults to the current year

month: Gregorian month of year, defaults to the current month

day: Gregorian day of month, defaults to the current day

#### See also

`HDATE_JULIAN`.

`HOUR`
`HOUR` compute hour part of fractional day

    HOUR(time)

#### Arguments

time: time of day as fractional day

#### Description

The `HOUR` function computes the hour part of the fractional day given by time.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TIME`, `MINUTE`, `SECOND`.

`ISOWEEKNUM`
`ISOWEEKNUM` ISO week number

    ISOWEEKNUM(date)

#### Arguments

date: date serial value

#### Description

`ISOWEEKNUM` calculates the week number according to the ISO 8601 standard. Weeks start on Mondays and week 1 contains the first Thursday of the year.

#### Note

January 1 of a year is sometimes in week 52 or 53 of the previous year. Similarly, December 31 is sometimes in week 1 of the following year.

#### See also

`ISOYEAR`, `WEEKNUM`.

`ISOYEAR`
`ISOYEAR` year corresponding to the ISO week number

    ISOYEAR(date)

#### Arguments

date: date serial value

#### Description

`ISOYEAR` calculates the year to go with week number according to the ISO 8601 standard.

#### Note

January 1 of a year is sometimes in week 52 or 53 of the previous year. Similarly, December 31 is sometimes in week 1 of the following year.

#### See also

`ISOWEEKNUM`, `YEAR`.

`MINUTE`
`MINUTE` compute minute part of fractional day

    MINUTE(time)

#### Arguments

time: time of day as fractional day

#### Description

The `MINUTE` function computes the minute part of the fractional day given by time.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TIME`, `HOUR`, `SECOND`.

`MONTH`
`MONTH` the month part of a date serial value

    MONTH(date)

#### Arguments

date: date serial value

#### Description

The `MONTH` function returns the month part of date.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATE`, `YEAR`, `DAY`.

`NETWORKDAYS`
`NETWORKDAYS` number of workdays in range

    NETWORKDAYS(start_date,end_date,holidays,weekend)

#### Arguments

start_date: starting date serial value

end_date: ending date serial value

holidays: array of holidays

weekend: array of 0s and 1s, indicating whether a weekday (S, M, T, W, T, F, S) is on the weekend, defaults to {1,0,0,0,0,0,1}

#### Description

`NETWORKDAYS` calculates the number of days from start_date to end_date skipping weekends and holidays in the process.

#### Note

If an entry of weekend is non-zero, the corresponding weekday is not a work day.

#### Microsoft Excel Compatibility

This function is Excel compatible if the last argument is omitted.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`WORKDAY`.

`NOW`
`NOW` the date and time serial value of the current time

    NOW()

#### Description

The `NOW` function returns the date and time serial value of the moment it is computed. Recomputing later will produce a different value.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATE`.

`PENTECOSTSUNDAY`
`PENTECOSTSUNDAY` Pentecost Sunday in the Gregorian calendar according to the Roman rite of the Christian Church

    PENTECOSTSUNDAY(year)

#### Arguments

year: year between 1582 and 9956, defaults to the year of the next Pentecost Sunday

#### Note

Two digit years are adjusted as elsewhere in Gnumeric. Dates before 1904 may also be prohibited.

#### See also

`EASTERSUNDAY`.

`SECOND`
`SECOND` compute seconds part of fractional day

    SECOND(time)

#### Arguments

time: time of day as fractional day

#### Description

The `SECOND` function computes the seconds part of the fractional day given by time.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TIME`, `HOUR`, `MINUTE`.

`TIME`
`TIME` create a time serial value

    TIME(hour,minute,second)

#### Arguments

hour: hour of the day

minute: minute within the hour

second: second within the minute

#### Description

The `TIME` function computes the fractional day between midnight at the time given by hour, minute, and second.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`HOUR`, `MINUTE`, `SECOND`.

`TIMEVALUE`
`TIMEVALUE` the time part of a date and time serial value

    TIMEVALUE(serial)

#### Arguments

serial: date and time serial value

#### Description

`TIMEVALUE` returns the time-of-day part of a date and time serial value.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATEVALUE`, `TIME`.

`TODAY`
`TODAY` the date serial value of today

    TODAY()

#### Description

The `TODAY` function returns the date serial value of the day it is computed. Recomputing on a later date will produce a different value.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATE`.

`UNIX2DATE`
`UNIX2DATE` date value corresponding to the Unix timestamp t

    UNIX2DATE(t)

#### Arguments

t: Unix time stamp

#### Description

The `UNIX2DATE` function translates Unix timestamps into the corresponding date. A Unix timestamp is the number of seconds since midnight (0:00) of January 1st, 1970 GMT.

#### See also

`DATE2UNIX`, `DATE`.

`WEEKDAY`
`WEEKDAY` day-of-week

    WEEKDAY(date,method)

#### Arguments

date: date serial value

method: numbering system, defaults to 1

#### Description

The `WEEKDAY` function returns the day-of-week of date. The value of method determines how days are numbered; it defaults to 1.

#### Note

If method is 1, then Sunday is 1, Monday is 2, etc. If method is 2, then Monday is 1, Tuesday is 2, etc. If method is 3, then Monday is 0, Tuesday is 1, etc.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATE`, `ISOWEEKNUM`.

`WEEKNUM`
`WEEKNUM` week number

    WEEKNUM(date,method)

#### Arguments

date: date serial value

method: numbering system, defaults to 1

#### Description

`WEEKNUM` calculates the week number according to method which defaults to 1.

#### Note

If method is 1, then weeks start on Sundays and January 1 is in week 1. If method is 2, then weeks start on Mondays and January 1 is in week 1. If method is 150, then the ISO 8601 numbering is used.

#### See also

`ISOWEEKNUM`.

`WORKDAY`
`WORKDAY` add working days

    WORKDAY(date,days,holidays,weekend)

#### Arguments

date: date serial value

days: number of days to add

holidays: array of holidays

weekend: array of 0s and 1s, indicating whether a weekday (S, M, T, W, T, F, S) is on the weekend, defaults to {1,0,0,0,0,0,1}

#### Description

`WORKDAY` adjusts date by days skipping over weekends and holidays in the process.

#### Note

days may be negative. If an entry of weekend is non-zero, the corresponding weekday is not a work day.

#### Microsoft Excel Compatibility

This function is Excel compatible if the last argument is omitted.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`NETWORKDAYS`.

`YEAR`
`YEAR` the year part of a date serial value

    YEAR(date)

#### Arguments

date: date serial value

#### Description

The `YEAR` function returns the year part of date.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DATE`, `MONTH`, `DAY`.

`YEARFRAC`
`YEARFRAC` fractional number of years between dates

    YEARFRAC(start_date,end_date,basis)

#### Arguments

start_date: starting date serial value

end_date: ending date serial value

basis: calendar basis

#### Description

`YEARFRAC` calculates the number of days from start_date to end_date according to the calendar specified by basis, which defaults to 0, and expresses the result as a fractional number of years.

#### Note

If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`DATE`.

## Engineering

`BASE`
`BASE` string of digits representing the number n in base b

    BASE(n,b,length)

#### Arguments

n: integer

b: base (2 ≤ b ≤ 36)

length: minimum length of the resulting string

#### Description

`BASE` converts n to its string representation in base b. Leading zeroes will be added to reach the minimum length given by length.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`DECIMAL`.

`BESSELI`
`BESSELI` Modified Bessel function of the first kind of order @{α} at x

    BESSELI(X,α)

#### Arguments

X: number

@{α}: order (any number)

#### Note

If x or @{α} are not numeric, #VALUE! is returned. If @{α} < 0, #NUM! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible if only integer orders @{α} are used.

#### See also

`BESSELJ`, `BESSELK`, `BESSELY`.

`BESSELJ`
`BESSELJ` Bessel function of the first kind of order @{α} at x

    BESSELJ(X,α)

#### Arguments

X: number

@{α}: order (any non-negative integer)

#### Note

If x or @{α} are not numeric, #VALUE! is returned. If @{α} < 0, #NUM! is returned. If @{α} is not an integer, it is truncated.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BESSELI`, `BESSELK`, `BESSELY`.

`BESSELK`
`BESSELK` Modified Bessel function of the second kind of order @{α} at x

    BESSELK(X,α)

#### Arguments

X: number

@{α}: order (any number)

#### Note

If x or @{α} are not numeric, #VALUE! is returned. If @{α} < 0, #NUM! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible if only integer orders @{α} are used.

#### See also

`BESSELI`, `BESSELJ`, `BESSELY`.

`BESSELY`
`BESSELY` Bessel function of the second kind of order @{α} at x

    BESSELY(X,α)

#### Arguments

X: number

@{α}: order (any non-negative integer)

#### Note

If x or @{α} are not numeric, #VALUE! is returned. If @{α} < 0, #NUM! is returned. If @{α} is not an integer, it is truncated.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BESSELI`, `BESSELJ`, `BESSELK`.

`BIN2DEC`
`BIN2DEC` decimal representation of the binary number x

    BIN2DEC(x)

#### Arguments

x: a binary number, either as a string or as a number involving only the digits 0 and 1

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DEC2BIN`, `BIN2OCT`, `BIN2HEX`.

`BIN2HEX`
`BIN2HEX` hexadecimal representation of the binary number x

    BIN2HEX(x,places)

#### Arguments

x: a binary number, either as a string or as a number involving only the digits 0 and 1

places: number of digits

#### Description

If places is given, `BIN2HEX` pads the result with zeros to achieve exactly places digits. If this is not possible, `BIN2HEX` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`HEX2BIN`, `BIN2OCT`, `BIN2DEC`.

`BIN2OCT`
`BIN2OCT` octal representation of the binary number x

    BIN2OCT(x,places)

#### Arguments

x: a binary number, either as a string or as a number involving only the digits 0 and 1

places: number of digits

#### Description

If places is given, `BIN2OCT` pads the result with zeros to achieve exactly places digits. If this is not possible, `BIN2OCT` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`OCT2BIN`, `BIN2DEC`, `BIN2HEX`.

`CONVERT`
`CONVERT` a converted measurement

    CONVERT(x,from,to)

#### Arguments

x: number

from: unit (string)

to: unit (string)

#### Description

`CONVERT` returns a conversion from one measurement system to another. x is a value in from units that is to be converted into to units.

from and to can be any of the following:

Weight and mass:

'g' Gram

'sg' Slug

'lbm' Pound

'u' U (atomic mass)

'ozm' Ounce

Distance:

'm' Meter

'mi' Statute mile

'Nmi' Nautical mile

'in' Inch

'ft' Foot

'yd' Yard

'ang' Angstrom

'Pica' Pica Points

'picapt' Pica Points

'pica' Pica

Time:

'yr' Year

'day' Day

'hr' Hour

'mn' Minute

'sec' Second

Pressure:

'Pa' Pascal

'atm' Atmosphere

'mmHg' mm of Mercury

Force:

'N' Newton

'dyn' Dyne

'lbf' Pound force

Energy:

'J' Joule

'e' Erg

'c' Thermodynamic calorie

'cal' IT calorie

'eV' Electron volt

'HPh' Horsepower-hour

'Wh' Watt-hour

'flb' Foot-pound

'BTU' BTU

Power:

'HP' Horsepower

'W' Watt

Magnetism:

'T' Tesla

'ga' Gauss

Temperature:

'C' Degree Celsius

'F' Degree Fahrenheit

'K' Degree Kelvin

Liquid measure:

'tsp' Teaspoon

'tbs' Tablespoon

'oz' Fluid ounce

'cup' Cup

'pt' Pint

'qt' Quart

'gal' Gallon

'l' Liter

For metric units any of the following prefixes can be used:

'Y' yotta 1E+24

'Z' zetta 1E+21

'E' exa 1E+18

'P' peta 1E+15

'T' tera 1E+12

'G' giga 1E+09

'M' mega 1E+06

'k' kilo 1E+03

'h' hecto 1E+02

'e' deca (deka) 1E+01

'd' deci 1E-01

'c' centi 1E-02

'm' milli 1E-03

'u' micro 1E-06

'n' nano 1E-09

'p' pico 1E-12

'f' femto 1E-15

'a' atto 1E-18

'z' zepto 1E-21

'y' yocto 1E-24

#### Note

If from and to are different types, `CONVERT` returns #N/A!

#### Microsoft Excel Compatibility

This function is Excel compatible (except "picapt").

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

`DEC2BIN`
`DEC2BIN` binary representation of the decimal number x

    DEC2BIN(x,places)

#### Arguments

x: integer

places: number of digits

#### Description

If places is given, `DEC2BIN` pads the result with zeros to achieve exactly places digits. If this is not possible, `DEC2BIN` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BIN2DEC`, `DEC2OCT`, `DEC2HEX`.

`DEC2HEX`
`DEC2HEX` hexadecimal representation of the decimal number x

    DEC2HEX(x,places)

#### Arguments

x: integer

places: number of digits

#### Description

If places is given, `DEC2HEX` pads the result with zeros to achieve exactly places digits. If this is not possible, `DEC2HEX` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`HEX2DEC`, `DEC2BIN`, `DEC2OCT`.

`DEC2OCT`
`DEC2OCT` octal representation of the decimal number x

    DEC2OCT(x,places)

#### Arguments

x: integer

places: number of digits

#### Description

If places is given, `DEC2OCT` pads the result with zeros to achieve exactly places digits. If this is not possible, `DEC2OCT` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`OCT2DEC`, `DEC2BIN`, `DEC2HEX`.

`DECIMAL`
`DECIMAL` decimal representation of x

    DECIMAL(x,base)

#### Arguments

x: number in base base

base: base of x, (2 ≤ base ≤ 36)

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`BASE`.

`DELTA`
`DELTA` Kronecker delta function

    DELTA(x0,x1)

#### Arguments

x0: number

x1: number, defaults to 0

#### Description

`DELTA` returns 1 if x1 = x0 and 0 otherwise.

#### Note

If either argument is non-numeric, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`EXACT`, `GESTEP`.

`ERF`
`ERF` Gauss error function

    ERF(lower,upper)

#### Arguments

lower: lower limit of the integral, defaults to 0

upper: upper limit of the integral

#### Description

`ERF` returns 2/sqrt(π)* integral from lower to upper of exp(-t*t) dt

#### Microsoft Excel Compatibility

This function is Excel compatible if two arguments are supplied and neither is negative.

#### See also

`ERFC`.

`ERFC`
`ERFC` Complementary Gauss error function

    ERFC(x)

#### Arguments

x: number

#### Description

`ERFC` returns 2/sqrt(π)* integral from x to ∞ of exp(-t*t) dt

#### See also

`ERF`.

`GESTEP`
`GESTEP` step function with step at x1 evaluated at x0

    GESTEP(x0,x1)

#### Arguments

x0: number

x1: number, defaults to 0

#### Description

`GESTEP` returns 1 if x1 ≤ x0 and 0 otherwise.

#### Note

If either argument is non-numeric, #VALUE! is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DELTA`.

`HEX2BIN`
`HEX2BIN` binary representation of the hexadecimal number x

    HEX2BIN(x,places)

#### Arguments

x: a hexadecimal number, either as a string or as a number if no A to F are needed

places: number of digits

#### Description

If places is given, `HEX2BIN` pads the result with zeros to achieve exactly places digits. If this is not possible, `HEX2BIN` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BIN2HEX`, `HEX2OCT`, `HEX2DEC`.

`HEX2DEC`
`HEX2DEC` decimal representation of the hexadecimal number x

    HEX2DEC(x)

#### Arguments

x: a hexadecimal number, either as a string or as a number if no A to F are needed

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DEC2HEX`, `HEX2BIN`, `HEX2OCT`.

`HEX2OCT`
`HEX2OCT` octal representation of the hexadecimal number x

    HEX2OCT(x,places)

#### Arguments

x: a hexadecimal number, either as a string or as a number if no A to F are needed

places: number of digits

#### Description

If places is given, `HEX2OCT` pads the result with zeros to achieve exactly places digits. If this is not possible, `HEX2OCT` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`OCT2HEX`, `HEX2BIN`, `HEX2DEC`.

`INVSUMINV`
`INVSUMINV` the reciprocal of the sum of reciprocals of the arguments

    INVSUMINV(x0,x1)

#### Arguments

x0: non-negative number

x1: non-negative number

#### Description

`INVSUMINV` sum calculates the reciprocal (the inverse) of the sum of reciprocals (inverses) of all its arguments.

#### Note

If any of the arguments is negative, #VALUE! is returned.

If any argument is zero, the result is zero.

#### See also

`HARMEAN`.

`OCT2BIN`
`OCT2BIN` binary representation of the octal number x

    OCT2BIN(x,places)

#### Arguments

x: a octal number, either as a string or as a number

places: number of digits

#### Description

If places is given, `OCT2BIN` pads the result with zeros to achieve exactly places digits. If this is not possible, `OCT2BIN` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BIN2OCT`, `OCT2DEC`, `OCT2HEX`.

`OCT2DEC`
`OCT2DEC` decimal representation of the octal number x

    OCT2DEC(x)

#### Arguments

x: a octal number, either as a string or as a number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DEC2OCT`, `OCT2BIN`, `OCT2HEX`.

`OCT2HEX`
`OCT2HEX` hexadecimal representation of the octal number x

    OCT2HEX(x,places)

#### Arguments

x: a octal number, either as a string or as a number

places: number of digits

#### Description

If places is given, `OCT2HEX` pads the result with zeros to achieve exactly places digits. If this is not possible, `OCT2HEX` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`HEX2OCT`, `OCT2BIN`, `OCT2DEC`.

## Erlang

`DIMCIRC`
`DIMCIRC` number of circuits required

    DIMCIRC(traffic,gos)

#### Arguments

traffic: number of calls

gos: grade of service

#### Description

`DIMCIRC` returns the number of circuits required given traffic calls with grade of service gos.

#### See also

`OFFCAP`, `OFFTRAF`, `PROBBLOCK`.

`OFFCAP`
`OFFCAP` traffic capacity

    OFFCAP(circuits,gos)

#### Arguments

circuits: number of circuits

gos: grade of service

#### Description

`OFFCAP` returns the traffic capacity given circuits circuits with grade of service gos.

#### See also

`DIMCIRC`, `OFFTRAF`, `PROBBLOCK`.

`OFFTRAF`
`OFFTRAF` predicted number of offered calls

    OFFTRAF(traffic,circuits)

#### Arguments

traffic: number of carried calls

circuits: number of circuits

#### Description

`OFFTRAF` returns the predicted number of offered calls given traffic carried calls (taken from measurements) on circuits circuits.

#### Note

traffic cannot exceed circuits.

#### See also

`PROBBLOCK`, `DIMCIRC`, `OFFCAP`.

`PROBBLOCK`
`PROBBLOCK` probability of blocking

    PROBBLOCK(traffic,circuits)

#### Arguments

traffic: number of calls

circuits: number of circuits

#### Description

`PROBBLOCK` returns probability of blocking when traffic calls load into circuits circuits.

#### Note

traffic cannot exceed circuits.

#### See also

`OFFTRAF`, `DIMCIRC`, `OFFCAP`.

## Finance

`ACCRINT`
`ACCRINT` accrued interest

    ACCRINT(issue,first_interest,settlement,rate,par,frequency,basis,calc_method)

#### Arguments

issue: date of issue

first_interest: date of first interest payment

settlement: settlement date

rate: nominal annual interest rate

par: par value, defaults to $1000

frequency: number of interest payments per year

basis: calendar basis, defaults to 0

calc_method: calculation method, defaults to TRUE

#### Description

If first_interest < settlement and calc_method is TRUE, then `ACCRINT` returns the sum of the interest accrued in all coupon periods from issue date until settlement date.

If first_interest < settlement and calc_method is FALSE, then `ACCRINT` returns the sum of the interest accrued in all coupon periods from first_interest date until settlement date.

Otherwise `ACCRINT` returns the sum of the interest accrued in all coupon periods from issue date until settlement date.

#### Note

frequency must be one of 1, 2 or 4, but the exact value does not affect the result. issue must precede both first_interest and settlement. frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`ACCRINTM`.

`ACCRINTM`
`ACCRINTM` accrued interest

    ACCRINTM(issue,maturity,rate,par,basis)

#### Arguments

issue: date of issue

maturity: maturity date

rate: nominal annual interest rate

par: par value

basis: calendar basis

#### Description

ACCRINT calculates the accrued interest from issue to maturity.

#### Note

par defaults to $1000. If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`ACCRINT`.

`AMORDEGRC`
`AMORDEGRC` depreciation of an asset using French accounting conventions

    AMORDEGRC(cost,purchase_date,first_period,salvage,period,rate,basis)

#### Arguments

cost: initial cost of asset

purchase_date: date of purchase

first_period: end of first period

salvage: value after depreciation

period: subject period

rate: depreciation rate

basis: calendar basis

#### Description

`AMORDEGRC` calculates the depreciation of an asset using French accounting conventions. Assets purchased in the middle of a period take prorated depreciation into account. This is similar to AMORLINC, except that a depreciation coefficient is applied in the calculation depending on the life of the assets.

The depreciation coefficient used is:

1 for an expected lifetime less than 3 years,

1.5 for an expected lifetime of at least 3 years but less than 5 years,

2 for an expected lifetime of at least 5 years but at most 6 years,

2.5 for an expected lifetime of more than 6 years.

#### Note

Special depreciation rules are applied for the last two periods resulting in a possible total depreciation exceeding the difference of cost - salvage. Named for AMORtissement DEGRessif Comptabilite. If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`AMORLINC`.

`AMORLINC`
`AMORLINC` depreciation of an asset using French accounting conventions

    AMORLINC(cost,purchase_date,first_period,salvage,period,rate,basis)

#### Arguments

cost: initial cost of asset

purchase_date: date of purchase

first_period: end of first period

salvage: value after depreciation

period: subject period

rate: depreciation rate

basis: calendar basis

#### Description

`AMORLINC` calculates the depreciation of an asset using French accounting conventions. Assets purchased in the middle of a period take prorated depreciation into account.

#### Note

Named for AMORtissement LINeaire Comptabilite. If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`AMORDEGRC`.

`ATL_LAST`
`ATL_LAST` sample real-time data source

    ATL_LAST(tag)

#### Arguments

tag: tag to watch

#### Description

`ATL_LAST` is a sample implementation of a real time data source. It takes a string tag and monitors the named pipe ~/atl for changes to the value of that tag.

#### Note

This is not intended to be generally enabled and is OFF by default.

`COUPDAYBS`
`COUPDAYBS` number of days from coupon period to settlement

    COUPDAYBS(settlement,maturity,frequency,basis,eom)

#### Arguments

settlement: settlement date

maturity: maturity date

frequency: number of interest payments per year

basis: calendar basis

eom: end-of-month flag

#### Description

`COUPDAYBS` calculates the number of days from the beginning of the coupon period to the settlement date.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`COUPDAYS`.

`COUPDAYS`
`COUPDAYS` number of days in the coupon period of the settlement date

    COUPDAYS(settlement,maturity,frequency,basis,eom)

#### Arguments

settlement: settlement date

maturity: maturity date

frequency: number of interest payments per year

basis: calendar basis

eom: end-of-month flag

#### Description

`COUPDAYS` calculates the number of days in the coupon period of the settlement date.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`COUPDAYBS`, `COUPDAYSNC`.

`COUPDAYSNC`
`COUPDAYSNC` number of days from the settlement date to the next coupon period

    COUPDAYSNC(settlement,maturity,frequency,basis,eom)

#### Arguments

settlement: settlement date

maturity: maturity date

frequency: number of interest payments per year

basis: calendar basis

eom: end-of-month flag

#### Description

`COUPDAYSNC` calculates number of days from the settlement date to the next coupon period.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`COUPDAYS`, `COUPDAYBS`.

`COUPNCD`
`COUPNCD` the next coupon date after settlement

    COUPNCD(settlement,maturity,frequency,basis,eom)

#### Arguments

settlement: settlement date

maturity: maturity date

frequency: number of interest payments per year

basis: calendar basis

eom: end-of-month flag

#### Description

`COUPNCD` calculates the coupon date following settlement.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`COUPPCD`, `COUPDAYS`, `COUPDAYBS`.

`COUPNUM`
`COUPNUM` number of coupons

    COUPNUM(settlement,maturity,frequency,basis,eom)

#### Arguments

settlement: settlement date

maturity: maturity date

frequency: number of interest payments per year

basis: calendar basis

eom: end-of-month flag

#### Description

`COUPNUM` calculates the number of coupons to be paid between the settlement and maturity dates, rounded up.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`COUPNCD`, `COUPPCD`.

`COUPPCD`
`COUPPCD` the last coupon date before settlement

    COUPPCD(settlement,maturity,frequency,basis,eom)

#### Arguments

settlement: settlement date

maturity: maturity date

frequency: number of interest payments per year

basis: calendar basis

eom: end-of-month flag

#### Description

`COUPPCD` calculates the coupon date preceding settlement.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`COUPNCD`, `COUPDAYS`, `COUPDAYBS`.

`CUM_BIV_NORM_DIST`
`CUM_BIV_NORM_DIST` cumulative bivariate normal distribution

    CUM_BIV_NORM_DIST(a,b,rho)

#### Arguments

a: limit for first random variable

b: limit for second random variable

rho: correlation of the two random variables

#### Description

`CUM_BIV_NORM_DIST` calculates the probability that two standard normal distributed random variables with correlation rho are respectively each less than a and b.

`CUMIPMT`
`CUMIPMT` cumulative interest payment

    CUMIPMT(rate,nper,pv,start_period,end_period,type)

#### Arguments

rate: interest rate per period

nper: number of periods

pv: present value

start_period: first period to accumulate for

end_period: last period to accumulate for

type: payment type

#### Description

`CUMIPMT` calculates the cumulative interest paid on a loan from start_period to end_period.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`IPMT`.

`CUMPRINC`
`CUMPRINC` cumulative principal

    CUMPRINC(rate,nper,pv,start_period,end_period,type)

#### Arguments

rate: interest rate per period

nper: number of periods

pv: present value

start_period: first period to accumulate for

end_period: last period to accumulate for

type: payment type

#### Description

`CUMPRINC` calculates the cumulative principal paid on a loan from start_period to end_period.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`PPMT`.

`DB`
`DB` depreciation of an asset

    DB(cost,salvage,life,period,month)

#### Arguments

cost: initial cost of asset

salvage: value after depreciation

life: number of periods

period: subject period

month: number of months in first year of depreciation

#### Description

`DB` calculates the depreciation of an asset for a given period using the fixed-declining balance method.

#### See also

`DDB`, `SLN`, `SYD`.

`DDB`
`DDB` depreciation of an asset

    DDB(cost,salvage,life,period,factor)

#### Arguments

cost: initial cost of asset

salvage: value after depreciation

life: number of periods

period: subject period

factor: factor at which the balance declines

#### Description

`DDB` calculates the depreciation of an asset for a given period using the double-declining balance method.

#### See also

`DB`, `SLN`, `SYD`.

`DISC`
`DISC` discount rate

    DISC(settlement,maturity,par,redemption,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

par: price per $100 face value

redemption: amount received at maturity

basis: calendar basis

#### Description

`DISC` calculates the discount rate for a security.

#### Note

redemption is the redemption value per $100 face value. If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`PRICEMAT`.

`DOLLARDE`
`DOLLARDE` convert to decimal dollar amount

    DOLLARDE(fractional_dollar,fraction)

#### Arguments

fractional_dollar: amount to convert

fraction: denominator

#### Description

`DOLLARDE` converts a fractional dollar amount into a decimal amount. This is the inverse of the DOLLARFR function.

#### See also

`DOLLARFR`.

`DOLLARFR`
`DOLLARFR` convert to dollar fraction

    DOLLARFR(decimal_dollar,fraction)

#### Arguments

decimal_dollar: amount to convert

fraction: denominator

#### Description

`DOLLARFR` converts a fractional dollar amount into a fraction which is represented as the digits after the decimal point. For example, 2/8 would be represented as .2 while 3/16 would be represented as .03.

#### See also

`DOLLARDE`.

`DURATION`
`DURATION` the duration of a security

    DURATION(settlement,maturity,coupon,yield,frequency,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

coupon: annual coupon rate

yield: annual yield of security

frequency: number of interest payments per year

basis: calendar basis

#### Description

`DURATION` calculates the duration of a security.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`MDURATION`.

`EFFECT`
`EFFECT` effective interest rate

    EFFECT(rate,nper)

#### Arguments

rate: nominal annual interest rate

nper: number of periods used for compounding

#### Description

`EFFECT` calculates the effective interest rate using the formula (1+rate/nper)^nper-1.

#### See also

`NOMINAL`.

`EURO`
`EURO` equivalent of 1 EUR

    EURO(currency)

#### Arguments

currency: three-letter currency code

#### Description

`EURO` calculates the national currency amount corresponding to 1 EUR for any of the national currencies that were replaced by the Euro on its introduction.

#### Note

currency must be one of ATS (Austria), BEF (Belgium), CYP (Cyprus), DEM (Germany), ESP (Spain), EUR (Euro), FIM (Finland), FRF (France), GRD (Greece), IEP (Ireland), ITL (Italy), LUF (Luxembourg), MTL (Malta), NLG (The Netherlands), PTE (Portugal), SIT (Slovenia), or SKK (Slovakia). This function is not likely to be useful anymore.

#### See also

`EUROCONVERT`.

`EUROCONVERT`
`EUROCONVERT` pre-Euro amount from one currency to another

    EUROCONVERT(n,source,target,full_precision,triangulation_precision)

#### Arguments

n: amount

source: three-letter source currency code

target: three-letter target currency code

full_precision: whether to provide the full precision; defaults to false

triangulation_precision: number of digits (at least 3) to be rounded to after conversion of the source currency to euro; defaults to no rounding

#### Description

`EUROCONVERT` converts n units of currency source to currency target. The rates used are the official ones used on the introduction of the Euro.

#### Note

If full_precision is true, the result is not rounded; if it false the result is rounded to 0 or 2 decimals depending on the target currency; defaults to false. source and target must be one of the currencies listed for the EURO function. This function is not likely to be useful anymore.

#### See also

`EURO`.

`FV`
`FV` future value

    FV(rate,nper,pmt,pv,type)

#### Arguments

rate: effective interest rate per period

nper: number of periods

pmt: payment at each period

pv: present value

type: payment type

#### Description

`FV` calculates the future value of pv moved nper periods into the future, assuming a periodic payment of pmt and an interest rate of rate per period.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`PV`.

`FVSCHEDULE`
`FVSCHEDULE` future value

    FVSCHEDULE(principal,schedule)

#### Arguments

principal: initial value

schedule: range of interest rates

#### Description

`FVSCHEDULE` calculates the future value of principal after applying a range of interest rates with compounding.

#### See also

`FV`.

`G_DURATION`
`G_DURATION` the duration of a investment

    G_DURATION(rate,pv,fv)

#### Arguments

rate: effective annual interest rate

pv: present value

fv: future value

#### Description

`G_DURATION` calculates the number of periods needed for an investment to attain a desired value.

#### OpenDocument Format (ODF) Compatibility

`G_DURATION` is the OpenFormula function PDURATION.

#### See also

`FV`, `PV`.

`INTRATE`
`INTRATE` interest rate

    INTRATE(settlement,maturity,investment,redemption,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

investment: amount paid on settlement

redemption: amount received at maturity

basis: calendar basis

#### Description

`INTRATE` calculates the interest of a fully vested security.

#### Note

If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`RECEIVED`.

`IPMT`
`IPMT` interest payment for period

    IPMT(rate,per,nper,pv,fv,type)

#### Arguments

rate: effective annual interest rate

per: period number

nper: number of periods

pv: present value

fv: future value

type: payment type

#### Description

`IPMT` calculates the interest part of an annuity's payment for period number per.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`PPMT`.

`IRR`
`IRR` internal rate of return

    IRR(values,guess)

#### Arguments

values: cash flow

guess: an estimate of what the result should be

#### Description

`IRR` calculates the internal rate of return of a cash flow with periodic payments. values lists the payments (negative values) and receipts (positive values) for each period.

#### Note

The optional guess is needed because there can be more than one valid result. It defaults to 10%.

#### See also

`XIRR`.

`ISPMT`
`ISPMT` interest payment for period

    ISPMT(rate,per,nper,pv)

#### Arguments

rate: effective annual interest rate

per: period number

nper: number of periods

pv: present value

#### Description

`ISPMT` calculates the interest payment for period number per.

#### See also

`PV`.

`MDURATION`
`MDURATION` the Macauley duration of a security

    MDURATION(settlement,maturity,coupon,yield,frequency,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

coupon: annual coupon rate

yield: annual yield of security

frequency: number of interest payments per year

basis: calendar basis

#### Description

`MDURATION` calculates the Macauley duration of a security.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`DURATION`.

`MIRR`
`MIRR` modified internal rate of return

    MIRR(values,finance_rate,reinvest_rate)

#### Arguments

values: cash flow

finance_rate: interest rate for financing cost

reinvest_rate: interest rate for reinvestments

#### Description

`MIRR` calculates the modified internal rate of return of a periodic cash flow.

#### See also

`IRR`, `XIRR`.

`NOMINAL`
`NOMINAL` nominal interest rate

    NOMINAL(rate,nper)

#### Arguments

rate: effective annual interest rate

nper: number of periods used for compounding

#### Description

`NOMINAL` calculates the nominal interest rate from the effective rate.

#### See also

`EFFECT`.

`NPER`
`NPER` number of periods

    NPER(rate,pmt,pv,fv,type)

#### Arguments

rate: effective annual interest rate

pmt: payment at each period

pv: present value

fv: future value

type: payment type

#### Description

`NPER` calculates the number of periods of an investment based on periodic constant payments and a constant interest rate.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`PV`, `FV`.

`NPV`
`NPV` net present value

    NPV(rate,value1,value2)

#### Arguments

rate: effective interest rate per period

value1: cash flow for period 1

value2: cash flow for period 2

#### Description

`NPV` calculates the net present value of a cash flow.

#### See also

`PV`.

`ODDFPRICE`
`ODDFPRICE` price of a security that has an odd first period

    ODDFPRICE(settlement,maturity,issue,first_interest,rate,yield,redemption,frequency,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

issue: date of issue

first_interest: first interest date

rate: nominal annual interest rate

yield: annual yield of security

redemption: amount received at maturity

frequency: number of interest payments per year

basis: calendar basis

#### Description

`ODDFPRICE` calculates the price per $100 face value of a security that pays periodic interest, but has an odd first period.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`ODDLPRICE`, `ODDFYIELD`.

`ODDFYIELD`
`ODDFYIELD` yield of a security that has an odd first period

    ODDFYIELD(settlement,maturity,issue,first_interest,rate,price,redemption,frequency,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

issue: date of issue

first_interest: first interest date

rate: nominal annual interest rate

price: price of security

redemption: amount received at maturity

frequency: number of interest payments per year

basis: calendar basis

#### Description

`ODDFYIELD` calculates the yield of a security that pays periodic interest, but has an odd first period.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`ODDFPRICE`, `ODDLYIELD`.

`ODDLPRICE`
`ODDLPRICE` price of a security that has an odd last period

    ODDLPRICE(settlement,maturity,last_interest,rate,yield,redemption,frequency,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

last_interest: last interest date

rate: nominal annual interest rate

yield: annual yield of security

redemption: amount received at maturity

frequency: number of interest payments per year

basis: calendar basis

#### Description

`ODDLPRICE` calculates the price per $100 face value of a security that pays periodic interest, but has an odd last period.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`YIELD`, `DURATION`.

`ODDLYIELD`
`ODDLYIELD` yield of a security that has an odd last period

    ODDLYIELD(settlement,maturity,last_interest,rate,price,redemption,frequency,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

last_interest: last interest date

rate: nominal annual interest rate

price: price of security

redemption: amount received at maturity

frequency: number of interest payments per year

basis: calendar basis

#### Description

`ODDLYIELD` calculates the yield of a security that pays periodic interest, but has an odd last period.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`YIELD`, `DURATION`.

`OPT_2_ASSET_CORRELATION`
`OPT_2_ASSET_CORRELATION` theoretical price of options on 2 assets with correlation rho

    OPT_2_ASSET_CORRELATION(call_put_flag,spot1,spot2,strike1,strike2,time,cost_of_carry1,cost_of_carry2,rate,volatility1,volatility2,rho)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot1: spot price of the underlying asset of the first option

spot2: spot price of the underlying asset of the second option

strike1: strike prices of the first option

strike2: strike prices of the second option

time: time to maturity in years

cost_of_carry1: net cost of holding the underlying asset of the first option (for common stocks, the risk free rate less the dividend yield)

cost_of_carry2: net cost of holding the underlying asset of the second option (for common stocks, the risk free rate less the dividend yield)

rate: annualized risk-free interest rate

volatility1: annualized volatility in price of the underlying asset of the first option

volatility2: annualized volatility in price of the underlying asset of the second option

rho: correlation between the two underlying assets

#### Description

`OPT_2_ASSET_CORRELATION` models the theoretical price of options on 2 assets with correlation rho. The payoff for a call is max(spot2 - strike2,0) if spot1 > strike1 or 0 otherwise. The payoff for a put is max (strike2 - spot2, 0) if spot1 < strike1 or 0 otherwise.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_AMER_EXCHANGE`
`OPT_AMER_EXCHANGE` theoretical price of an American option to exchange assets

    OPT_AMER_EXCHANGE(spot1,spot2,qty1,qty2,time,rate,cost_of_carry1,cost_of_carry2,volatility1,volatility2,rho)

#### Arguments

spot1: spot price of asset 1

spot2: spot price of asset 1

qty1: quantity of asset 1

qty2: quantity of asset 2

time: time to maturity in years

rate: annualized risk-free interest rate

cost_of_carry1: net cost of holding asset 1 (for common stocks, the risk free rate less the dividend yield)

cost_of_carry2: net cost of holding asset 2 (for common stocks, the risk free rate less the dividend yield)

volatility1: annualized volatility in price of asset 1

volatility2: annualized volatility in price of asset 2

rho: correlation between the prices of the two assets

#### Description

`OPT_AMER_EXCHANGE` models the theoretical price of an American option to exchange one asset with quantity qty2 and spot price spot2 for another with quantity qty1 and spot price spot1.

#### See also

`OPT_EURO_EXCHANGE`, `OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_BAW_AMER`
`OPT_BAW_AMER` theoretical price of an option according to the Barone Adesie & Whaley approximation

    OPT_BAW_AMER(call_put_flag,spot,strike,time,rate,cost_of_carry,volatility)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in days

rate: annualized risk-free interest rate

cost_of_carry: net cost of holding the underlying asset

volatility: annualized volatility of the asset

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_BINOMIAL`
`OPT_BINOMIAL` theoretical price of either an American or European style option using a binomial tree

    OPT_BINOMIAL(amer_euro_flag,call_put_flag,num_time_steps,spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

amer_euro_flag: 'a' for an American style option or 'e' for a European style option

call_put_flag: 'c' for a call and 'p' for a put

num_time_steps: number of time steps used in the valuation

spot: spot price

strike: strike price

time: time to maturity in years

rate: annualized risk-free interest rate

volatility: annualized volatility of the asset

cost_of_carry: net cost of holding the underlying asset

#### Note

A larger num_time_steps yields greater accuracy but `OPT_BINOMIAL` is slower to calculate.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_BJER_STENS`
`OPT_BJER_STENS` theoretical price of American options according to the Bjerksund & Stensland approximation technique

    OPT_BJER_STENS(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in days

rate: annualized risk-free interest rate

volatility: annualized volatility of the asset

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_BS`
`OPT_BS` price of a European option

    OPT_BS(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in years

rate: risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### Description

`OPT_BS` uses the Black-Scholes model to calculate the price of a European option struck at strike on an asset with spot price spot.

#### Note

The returned value will be expressed in the same units as strike and spot.

#### See also

`OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_VEGA`, `OPT_BS_GAMMA`.

`OPT_BS_CARRYCOST`
`OPT_BS_CARRYCOST` elasticity of a European option

    OPT_BS_CARRYCOST(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in years

rate: risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### Description

`OPT_BS_CARRYCOST` uses the Black-Scholes model to calculate the 'elasticity' of a European option struck at strike on an asset with spot price spot. The elasticity of an option is the rate of change of its price with respect to its cost_of_carry.

#### Note

Elasticity is expressed as the rate of change of the option value, per 100% volatility.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_BS_DELTA`
`OPT_BS_DELTA` delta of a European option

    OPT_BS_DELTA(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in years

rate: risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### Description

`OPT_BS_DELTA` uses the Black-Scholes model to calculate the 'delta' of a European option struck at strike on an asset with spot price spot.

#### Note

The returned value will be expressed in the same units as strike and spot.

#### See also

`OPT_BS`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_VEGA`, `OPT_BS_GAMMA`.

`OPT_BS_GAMMA`
`OPT_BS_GAMMA` gamma of a European option

    OPT_BS_GAMMA(spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

spot: spot price

strike: strike price

time: time to maturity in years

rate: risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### Description

`OPT_BS_GAMMA` uses the Black-Scholes model to calculate the 'gamma' of a European option struck at strike on an asset with spot price spot. The gamma of an option is the second derivative of its price with respect to the price of the underlying asset.

#### Note

Gamma is expressed as the rate of change of delta per unit change in spot. Gamma is the same for calls and puts.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_VEGA`.

`OPT_BS_RHO`
`OPT_BS_RHO` rho of a European option

    OPT_BS_RHO(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in years

rate: risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### Description

`OPT_BS_RHO` uses the Black-Scholes model to calculate the 'rho' of a European option struck at strike on an asset with spot price spot. The rho of an option is the rate of change of its price with respect to the risk free interest rate.

#### Note

Rho is expressed as the rate of change of the option value, per 100% change in rate.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_THETA`, `OPT_BS_VEGA`, `OPT_BS_GAMMA`.

`OPT_BS_THETA`
`OPT_BS_THETA` theta of a European option

    OPT_BS_THETA(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in years

rate: risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### Description

OPT_BS_DELTA uses the Black-Scholes model to calculate the 'theta' of a European option struck at strike on an asset with spot price spot. The theta of an option is the rate of change of its price with respect to time to expiry.

#### Note

Theta is expressed as the negative of the rate of change of the option value, per 365.25 days.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_VEGA`, `OPT_BS_GAMMA`.

`OPT_BS_VEGA`
`OPT_BS_VEGA` vega of a European option

    OPT_BS_VEGA(spot,strike,time,rate,volatility,cost_of_carry)

#### Arguments

spot: spot price

strike: strike price

time: time to maturity in years

rate: risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### Description

`OPT_BS_VEGA` uses the Black-Scholes model to calculate the 'vega' of a European option struck at strike on an asset with spot price spot. The vega of an option is the rate of change of its price with respect to volatility.

#### Note

Vega is the same for calls and puts. Vega is expressed as the rate of change of option value, per 100% volatility.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_COMPLEX_CHOOSER`
`OPT_COMPLEX_CHOOSER` theoretical price of a complex chooser option

    OPT_COMPLEX_CHOOSER(spot,strike_call,strike_put,time,time_call,time_put,rate,cost_of_carry,volatility)

#### Arguments

spot: spot price

strike_call: strike price, if exercised as a call option

strike_put: strike price, if exercised as a put option

time: time in years until the holder chooses a put or a call option

time_call: time in years to maturity of the call option if chosen

time_put: time in years to maturity of the put option if chosen

rate: annualized risk-free interest rate

cost_of_carry: net cost of holding the underlying asset

volatility: annualized volatility of the asset in percent for the period through to the exercise date

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_EURO_EXCHANGE`
`OPT_EURO_EXCHANGE` theoretical price of a European option to exchange assets

    OPT_EURO_EXCHANGE(spot1,spot2,qty1,qty2,time,rate,cost_of_carry1,cost_of_carry2,volatility1,volatility2,rho)

#### Arguments

spot1: spot price of asset 1

spot2: spot price of asset 1

qty1: quantity of asset 1

qty2: quantity of asset 2

time: time to maturity in years

rate: annualized risk-free interest rate

cost_of_carry1: net cost of holding asset 1 (for common stocks, the risk free rate less the dividend yield)

cost_of_carry2: net cost of holding asset 2 (for common stocks, the risk free rate less the dividend yield)

volatility1: annualized volatility in price of asset 1

volatility2: annualized volatility in price of asset 2

rho: correlation between the prices of the two assets

#### Description

`OPT_EURO_EXCHANGE` models the theoretical price of a European option to exchange one asset with quantity qty2 and spot price spot2 for another with quantity qty1 and spot price spot1.

#### See also

`OPT_AMER_EXCHANGE`, `OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_EXEC`
`OPT_EXEC` theoretical price of executive stock options

    OPT_EXEC(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry,lambda)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in days

rate: annualized risk-free interest rate

volatility: annualized volatility of the asset

cost_of_carry: net cost of holding the underlying asset

lambda: jump rate for executives

#### Note

The model assumes executives forfeit their options if they leave the company.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_EXTENDIBLE_WRITER`
`OPT_EXTENDIBLE_WRITER` theoretical price of extendible writer options

    OPT_EXTENDIBLE_WRITER(call_put_flag,spot,strike1,strike2,time1,time2,rate,cost_of_carry,volatility)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike1: strike price at which the option is struck

strike2: strike price at which the option is re-struck if out of the money at time1

time1: initial maturity of the option in years

time2: extended maturity in years if chosen

rate: annualized risk-free interest rate

cost_of_carry: net cost of holding the underlying asset

volatility: annualized volatility of the asset

#### Description

`OPT_EXTENDIBLE_WRITER` models the theoretical price of extendible writer options. These are options that have their maturity extended to time2 if the option is out of the money at time1.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_FIXED_STRK_LKBK`
`OPT_FIXED_STRK_LKBK` theoretical price of a fixed-strike lookback option

    OPT_FIXED_STRK_LKBK(call_put_flag,spot,spot_min,spot_max,strike,time,rate,cost_of_carry,volatility)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

spot_min: minimum spot price of the underlying asset so far observed

spot_max: maximum spot price of the underlying asset so far observed

strike: strike price

time: time to maturity in years

rate: annualized risk-free interest rate

cost_of_carry: net cost of holding the underlying asset

volatility: annualized volatility of the asset

#### Description

`OPT_FIXED_STRK_LKBK` determines the theoretical price of a fixed-strike lookback option where the holder of the option may exercise on expiry at the most favourable price observed during the options life of the underlying asset.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_FLOAT_STRK_LKBK`
`OPT_FLOAT_STRK_LKBK` theoretical price of floating-strike lookback option

    OPT_FLOAT_STRK_LKBK(call_put_flag,spot,spot_min,spot_max,time,rate,cost_of_carry,volatility)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

spot_min: minimum spot price of the underlying asset so far observed

spot_max: maximum spot price of the underlying asset so far observed

time: time to maturity in years

rate: annualized risk-free interest rate

cost_of_carry: net cost of holding the underlying asset

volatility: annualized volatility of the asset

#### Description

`OPT_FLOAT_STRK_LKBK` determines the theoretical price of a floating-strike lookback option where the holder of the option may exercise on expiry at the most favourable price observed during the options life of the underlying asset.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_FORWARD_START`
`OPT_FORWARD_START` theoretical price of forward start options

    OPT_FORWARD_START(call_put_flag,spot,alpha,time_start,time,rate,volatility,cost_of_carry)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

alpha: fraction setting the strike price at the future date time_start

time_start: time until the option starts in days

time: time to maturity in days

rate: annualized risk-free interest rate

volatility: annualized volatility of the asset

cost_of_carry: net cost of holding the underlying asset

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_FRENCH`
`OPT_FRENCH` theoretical price of a European option adjusted for trading day volatility

    OPT_FRENCH(call_put_flag,spot,strike,time,ttime,rate,volatility,cost_of_carry)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: ratio of the number of calendar days to exercise and the number of calendar days in the year

ttime: ratio of the number of trading days to exercise and the number of trading days in the year

rate: risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

cost_of_carry: net cost of holding the underlying asset (for common stocks, the risk free rate less the dividend yield), defaults to 0

#### Description

`OPT_FRENCH` values the theoretical price of a European option adjusted for trading day volatility, struck at strike on an asset with spot price spot.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_GARMAN_KOHLHAGEN`
`OPT_GARMAN_KOHLHAGEN` theoretical price of a European currency option

    OPT_GARMAN_KOHLHAGEN(call_put_flag,spot,strike,time,domestic_rate,foreign_rate,volatility)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: number of days to exercise

domestic_rate: domestic risk-free interest rate to the exercise date in percent

foreign_rate: foreign risk-free interest rate to the exercise date in percent

volatility: annualized volatility of the asset in percent for the period through to the exercise date

#### Description

`OPT_GARMAN_KOHLHAGEN` values the theoretical price of a European currency option struck at strike on an asset with spot price spot.

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_JUMP_DIFF`
`OPT_JUMP_DIFF` theoretical price of an option according to the Jump Diffusion process

    OPT_JUMP_DIFF(call_put_flag,spot,strike,time,rate,volatility,lambda,gamma)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time: time to maturity in years

rate: the annualized rate of interest

volatility: annualized volatility of the asset in percent for the period through to the exercise date

lambda: expected number of 'jumps' per year

gamma: proportion of volatility explained by the 'jumps'

#### Description

`OPT_JUMP_DIFF` models the theoretical price of an option according to the Jump Diffusion process (Merton).

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_MILTERSEN_SCHWARTZ`
`OPT_MILTERSEN_SCHWARTZ` theoretical price of options on commodities futures according to Miltersen & Schwartz

    OPT_MILTERSEN_SCHWARTZ(call_put_flag,p_t,f_t,strike,t1,t2,v_s,v_e,v_f,rho_se,rho_sf,rho_ef,kappa_e,kappa_f)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

p_t: zero coupon bond with expiry at option maturity

f_t: futures price

strike: strike price

t1: time to maturity of the option

t2: time to maturity of the underlying commodity futures contract

v_s: volatility of the spot commodity price

v_e: volatility of the future convenience yield

v_f: volatility of the forward rate of interest

rho_se: correlation between the spot commodity price and the convenience yield

rho_sf: correlation between the spot commodity price and the forward interest rate

rho_ef: correlation between the forward interest rate and the convenience yield

kappa_e: speed of mean reversion of the convenience yield

kappa_f: speed of mean reversion of the forward interest rate

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_ON_OPTIONS`
`OPT_ON_OPTIONS` theoretical price of options on options

    OPT_ON_OPTIONS(type_flag,spot,strike1,strike2,time1,time2,rate,cost_of_carry,volatility)

#### Arguments

type_flag: 'cc' for calls on calls, 'cp' for calls on puts, and so on for 'pc', and 'pp'

spot: spot price

strike1: strike price at which the option being valued is struck

strike2: strike price at which the underlying option is struck

time1: time in years to maturity of the option

time2: time in years to the maturity of the underlying option

rate: annualized risk-free interest rate

cost_of_carry: net cost of holding the underlying asset of the underlying option

volatility: annualized volatility in price of the underlying asset of the underlying option

#### Note

For common stocks, cost_of_carry is the risk free rate less the dividend yield. time2 ≥ time1

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_RGW`
`OPT_RGW` theoretical price of an American option according to the Roll-Geske-Whaley approximation

    OPT_RGW(spot,strike,time_payout,time_exp,rate,d,volatility)

#### Arguments

spot: spot price

strike: strike price

time_payout: time to dividend payout

time_exp: time to expiration

rate: annualized interest rate

d: amount of the dividend to be paid expressed in currency

volatility: annualized volatility of the asset in percent for the period through to the exercise date

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_SIMPLE_CHOOSER`
`OPT_SIMPLE_CHOOSER` theoretical price of a simple chooser option

    OPT_SIMPLE_CHOOSER(call_put_flag,spot,strike,time1,time2,cost_of_carry,volatility)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

time1: time in years until the holder chooses a put or a call option

time2: time in years until the chosen option expires

cost_of_carry: net cost of holding the underlying asset

volatility: annualized volatility of the asset

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_SPREAD_APPROX`
`OPT_SPREAD_APPROX` theoretical price of a European option on the spread between two futures contracts

    OPT_SPREAD_APPROX(call_put_flag,fut_price1,fut_price2,strike,time,rate,volatility1,volatility2,rho)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

fut_price1: price of the first futures contract

fut_price2: price of the second futures contract

strike: strike price

time: time to maturity in years

rate: annualized risk-free interest rate

volatility1: annualized volatility in price of the first underlying futures contract

volatility2: annualized volatility in price of the second underlying futures contract

rho: correlation between the two futures contracts

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`OPT_TIME_SWITCH`
`OPT_TIME_SWITCH` theoretical price of time switch options

    OPT_TIME_SWITCH(call_put_flag,spot,strike,a,time,m,dt,rate,cost_of_carry,volatility)

#### Arguments

call_put_flag: 'c' for a call and 'p' for a put

spot: spot price

strike: strike price

a: amount received for each time period

time: time to maturity in years

m: number of time units the option has already met the condition

dt: agreed upon discrete time period expressed as a fraction of a year

rate: annualized risk-free interest rate

cost_of_carry: net cost of holding the underlying asset

volatility: annualized volatility of the asset

#### Description

`OPT_TIME_SWITCH` models the theoretical price of time switch options. (Pechtl 1995). The holder receives a * dt for each period that the asset price was greater than strike (for a call) or below it (for a put).

#### See also

`OPT_BS`, `OPT_BS_DELTA`, `OPT_BS_RHO`, `OPT_BS_THETA`, `OPT_BS_GAMMA`.

`PMT`
`PMT` payment for annuity

    PMT(rate,nper,pv,fv,type)

#### Arguments

rate: effective annual interest rate

nper: number of periods

pv: present value

fv: future value

type: payment type

#### Description

`PMT` calculates the payment amount for an annuity.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`PV`, `FV`, `RATE`, `ISPMT`.

`PPMT`
`PPMT` interest payment for period

    PPMT(rate,per,nper,pv,fv,type)

#### Arguments

rate: effective annual interest rate

per: period number

nper: number of periods

pv: present value

fv: future value

type: payment type

#### Description

`PPMT` calculates the principal part of an annuity's payment for period number per.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`IPMT`.

`PRICE`
`PRICE` price of a security

    PRICE(settlement,maturity,rate,yield,redemption,frequency,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

rate: nominal annual interest rate

yield: annual yield of security

redemption: amount received at maturity

frequency: number of interest payments per year

basis: calendar basis

#### Description

`PRICE` calculates the price per $100 face value of a security that pays periodic interest.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`YIELD`, `DURATION`.

`PRICEDISC`
`PRICEDISC` discounted price

    PRICEDISC(settlement,maturity,discount,redemption,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

discount: annual rate at which to discount

redemption: amount received at maturity

basis: calendar basis

#### Description

`PRICEDISC` calculates the price per $100 face value of a bond that does not pay interest at maturity.

#### Note

If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`PRICEMAT`.

`PRICEMAT`
`PRICEMAT` price at maturity

    PRICEMAT(settlement,maturity,issue,discount,yield,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

issue: date of issue

discount: annual rate at which to discount

yield: annual yield of security

basis: calendar basis

#### Description

`PRICEMAT` calculates the price per $100 face value of a bond that pays interest at maturity.

#### Note

If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`PRICEDISC`.

`PV`
`PV` present value

    PV(rate,nper,pmt,fv,type)

#### Arguments

rate: effective interest rate per period

nper: number of periods

pmt: payment at each period

fv: future value

type: payment type

#### Description

`PV` calculates the present value of fv which is nper periods into the future, assuming a periodic payment of pmt and an interest rate of rate per period.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`FV`.

`RATE`
`RATE` rate of investment

    RATE(nper,pmt,pv,fv,type,guess)

#### Arguments

nper: number of periods

pmt: payment at each period

pv: present value

fv: future value

type: payment type

guess: an estimate of what the result should be

#### Description

`RATE` calculates the rate of return.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period. The optional guess is needed because there can be more than one valid result. It defaults to 10%.

#### See also

`PV`, `FV`.

`RECEIVED`
`RECEIVED` amount to be received at maturity

    RECEIVED(settlement,maturity,investment,rate,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

investment: amount paid on settlement

rate: nominal annual interest rate

basis: calendar basis

#### Description

`RECEIVED` calculates the amount to be received when a security matures.

#### Note

If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`INTRATE`.

`RRI`
`RRI` equivalent interest rate for an investment increasing in value

    RRI(p,pv,fv)

#### Arguments

p: number of periods

pv: present value

fv: future value

#### Description

`RRI` determines an equivalent interest rate for an investment that increases in value. The interest is compounded after each complete period.

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period. Note that p need not be an integer but for fractional value the calculated rate is only approximate.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`PV`, `FV`, `RATE`.

`SLN`
`SLN` depreciation of an asset

    SLN(cost,salvage,life)

#### Arguments

cost: initial cost of asset

salvage: value after depreciation

life: number of periods

#### Description

`SLN` calculates the depreciation of an asset using the straight-line method.

#### See also

`DB`, `DDB`, `SYD`.

`SYD`
`SYD` sum-of-years depreciation

    SYD(cost,salvage,life,period)

#### Arguments

cost: initial cost of asset

salvage: value after depreciation

life: number of periods

period: subject period

#### Description

`SYD` calculates the depreciation of an asset using the sum-of-years method.

#### See also

`DB`, `DDB`, `SLN`.

`TBILLEQ`
`TBILLEQ` bond-equivalent yield for a treasury bill

    TBILLEQ(settlement,maturity,discount)

#### Arguments

settlement: settlement date

maturity: maturity date

discount: annual rate at which to discount

#### Description

`TBILLEQ` calculates the bond-equivalent yield for a treasury bill.

#### See also

`TBILLPRICE`, `TBILLYIELD`.

`TBILLPRICE`
`TBILLPRICE` price of a treasury bill

    TBILLPRICE(settlement,maturity,discount)

#### Arguments

settlement: settlement date

maturity: maturity date

discount: annual rate at which to discount

#### Description

`TBILLPRICE` calculates the price per $100 face value for a treasury bill.

#### See also

`TBILLEQ`, `TBILLYIELD`.

`TBILLYIELD`
`TBILLYIELD` yield of a treasury bill

    TBILLYIELD(settlement,maturity,price)

#### Arguments

settlement: settlement date

maturity: maturity date

price: price

#### Description

`TBILLYIELD` calculates the yield of a treasury bill.

#### See also

`TBILLEQ`, `TBILLPRICE`.

`VDB`
`VDB` depreciation of an asset

    VDB(cost,salvage,life,start_period,end_period,factor,no_switch)

#### Arguments

cost: initial cost of asset

salvage: value after depreciation

life: number of periods

start_period: first period to accumulate for

end_period: last period to accumulate for

factor: factor at which the balance declines

no_switch: do not switch to straight-line depreciation

#### Description

`VDB` calculates the depreciation of an asset for a given period range using the variable-rate declining balance method.

#### Note

If no_switch is FALSE, the calculation switches to straight-line depreciation when depreciation is greater than the declining balance calculation.

#### See also

`DB`, `DDB`.

`XIRR`
`XIRR` internal rate of return

    XIRR(values,dates,guess)

#### Arguments

values: cash flow

dates: dates of cash flow

guess: an estimate of what the result should be

#### Description

`XIRR` calculates the annualized internal rate of return of a cash flow at arbitrary points in time. values lists the payments (negative values) and receipts (positive values) with one value for each entry in dates.

#### Note

The optional guess is needed because there can be more than one valid result. It defaults to 10%.

#### See also

`IRR`.

`XNPV`
`XNPV` net present value

    XNPV(rate,values,dates)

#### Arguments

rate: effective annual interest rate

values: cash flow

dates: dates of cash flow

#### Description

`XNPV` calculates the net present value of a cash flow at irregular times

#### Note

If type is 0, the default, payment is at the end of each period. If type is 1, payment is at the beginning of each period.

#### See also

`NPV`.

`YIELD`
`YIELD` yield of a security

    YIELD(settlement,maturity,rate,price,redemption,frequency,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

rate: nominal annual interest rate

price: price of security

redemption: amount received at maturity

frequency: number of interest payments per year

basis: calendar basis

#### Description

`YIELD` calculates the yield of a security that pays periodic interest.

#### Note

frequency may be 1 (annual), 2 (semi-annual), or 4 (quarterly). If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`PRICE`, `DURATION`.

`YIELDDISC`
`YIELDDISC` yield of a discounted security

    YIELDDISC(settlement,maturity,price,redemption,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

price: price of security

redemption: amount received at maturity

basis: calendar basis

#### Description

`YIELDDISC` calculates the yield of a discounted security.

#### Note

If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`PRICE`, `DURATION`.

`YIELDMAT`
`YIELDMAT` yield of a security

    YIELDMAT(settlement,maturity,issue,rate,price,basis)

#### Arguments

settlement: settlement date

maturity: maturity date

issue: date of issue

rate: nominal annual interest rate

price: price of security

basis: calendar basis

#### Description

`YIELDMAT` calculates the yield of a security for which the interest is paid at maturity date.

#### Note

If basis is 0, then the US 30/360 method is used. If basis is 1, then actual number of days is used. If basis is 2, then actual number of days is used within a month, but years are considered only 360 days. If basis is 3, then actual number of days is used within a month, but years are always considered 365 days. If basis is 4, then the European 30/360 method is used.

#### See also

`YIELDDISC`, `YIELD`.

## Gnumeric

`GNUMERIC_VERSION`
`GNUMERIC_VERSION` the current version of Gnumeric

    GNUMERIC_VERSION()

#### Description

`GNUMERIC_VERSION` returns the version of gnumeric as a string.

## Information

`CELL`
`CELL` information of type about cell

    CELL(type,cell)

#### Arguments

type: string specifying the type of information requested

cell: cell reference

#### Description

type specifies the type of information you want to obtain:

address Returns the given cell reference as text.

col Returns the number of the column in cell.

color Returns 0.

contents Returns the contents of the cell in cell.

column Returns the number of the column in cell.

columnwidth Returns the column width.

coord Returns the absolute address of cell.

datatype same as type

filename Returns the name of the file of cell.

format Returns the code of the format of the cell.

formulatype same as type

locked Returns 1 if cell is locked.

parentheses Returns 1 if cell contains a negative value

and its format displays it with parentheses.

prefix Returns a character indicating the horizontal

alignment of cell.

prefixcharacter same as prefix

protect Returns 1 if cell is locked.

row Returns the number of the row in cell.

sheetname Returns the name of the sheet of cell.

type Returns "l" if cell contains a string,

"v" if it contains some other value, and

"b" if cell is blank.

value Returns the contents of the cell in cell.

width Returns the column width.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`INDIRECT`.

`COUNTBLANK`
`COUNTBLANK` the number of blank cells in range

    COUNTBLANK(range)

#### Arguments

range: a cell range

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COUNT`.

`ERROR`
`ERROR` the error with the given name

    ERROR(name)

#### Arguments

name: string

#### See also

`ISERROR`.

`ERROR.TYPE`
`ERROR.TYPE` the type of error

    ERROR.TYPE(error)

#### Arguments

error: an error

#### Description

`ERROR.TYPE` returns an error number corresponding to the given error value. The error numbers for error values are:

#DIV/0! 2

#VALUE! 3

#REF! 4

#NAME? 5

#NUM! 6

#N/A 7

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ISERROR`.

`EXPRESSION`
`EXPRESSION` expression in cell as a string

    EXPRESSION(cell)

#### Arguments

cell: a cell reference

#### Note

If cell contains no expression, `EXPRESSION` returns empty.

#### See also

`TEXT`.

`GET.FORMULA`
`GET.FORMULA` the formula in cell as a string

    GET.FORMULA(cell)

#### Arguments

cell: the referenced cell

#### OpenDocument Format (ODF) Compatibility

`GET.FORMULA` is the OpenFormula function FORMULA.

#### See also

`EXPRESSION`, `ISFORMULA`.

`GET.LINK`
`GET.LINK` the target of the hyperlink attached to cell as a string

    GET.LINK(cell)

#### Arguments

cell: the referenced cell

#### Note

The value return is not updated automatically when the link attached to cell changes but requires a recalculation.

#### See also

`HYPERLINK`.

`GETENV`
`GETENV` the value of execution environment variable name

    GETENV(name)

#### Arguments

name: the name of the environment variable

#### Note

If a variable called name does not exist, #N/A! will be returned. Variable names are case sensitive.

`INFO`
`INFO` information about the current operating environment according to type

    INFO(type)

#### Arguments

type: string giving the type of information requested

#### Description

`INFO` returns information about the current operating environment according to type:

memavail Returns the amount of memory available, bytes.

memused Returns the amount of memory used (bytes).

numfile Returns the number of active worksheets.

osversion Returns the operating system version.

recalc Returns the recalculation mode (automatic).

release Returns the version of Gnumeric as text.

system Returns the name of the environment.

totmem Returns the amount of total memory available.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CELL`.

`ISBLANK`
`ISBLANK` TRUE if value is blank

    ISBLANK(value)

#### Arguments

value: a value

#### Description

This function checks if a value is blank. Empty cells are blank, but empty strings are not.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`ISERR`
`ISERR` TRUE if value is any error value except #N/A

    ISERR(value)

#### Arguments

value: a value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ISERROR`.

`ISERROR`
`ISERROR` TRUE if value is any error value

    ISERROR(value)

#### Arguments

value: a value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ISERR`, `ISNA`.

`ISEVEN`
`ISEVEN` TRUE if n is even

    ISEVEN(n)

#### Arguments

n: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ISODD`.

`ISFORMULA`
`ISFORMULA` TRUE if cell contains a formula

    ISFORMULA(cell)

#### Arguments

cell: the referenced cell

#### OpenDocument Format (ODF) Compatibility

`ISFORMULA` is OpenFormula compatible.

#### See also

`GET.FORMULA`.

`ISLOGICAL`
`ISLOGICAL` TRUE if value is a logical value

    ISLOGICAL(value)

#### Arguments

value: a value

#### Description

This function checks if a value is either TRUE or FALSE.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`ISNA`
`ISNA` TRUE if value is the #N/A error value

    ISNA(value)

#### Arguments

value: a value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`NA`.

`ISNONTEXT`
`ISNONTEXT` TRUE if value is not text

    ISNONTEXT(value)

#### Arguments

value: a value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ISTEXT`.

`ISNUMBER`
`ISNUMBER` TRUE if value is a number

    ISNUMBER(value)

#### Arguments

value: a value

#### Description

This function checks if a value is a number. Neither TRUE nor FALSE are numbers for this purpose.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`ISODD`
`ISODD` TRUE if n is odd

    ISODD(n)

#### Arguments

n: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ISEVEN`.

`ISREF`
`ISREF` TRUE if value is a reference

    ISREF(value)

#### Arguments

value: a value

#### Description

This function checks if a value is a cell reference.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`ISTEXT`
`ISTEXT` TRUE if value is text

    ISTEXT(value)

#### Arguments

value: a value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ISNONTEXT`.

`N`
`N` text converted to a number

    N(text)

#### Arguments

text: string

#### Note

If text contains non-numerical text, 0 is returned.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`NA`
`NA` the error value #N/A

    NA()

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ISNA`.

`TYPE`
`TYPE` a number indicating the data type of value

    TYPE(value)

#### Arguments

value: a value

#### Description

`TYPE` returns a number indicating the data type of value:

1 = number

2 = text

4 = boolean

16 = error

64 = array

#### Microsoft Excel Compatibility

This function is Excel compatible.

## Logic

`AND`
`AND` logical conjunction

    AND(b0,b1)

#### Arguments

b0: logical value

b1: logical value

#### Description

`AND` calculates the logical conjunction of its arguments b0,b1,...

#### Note

If an argument is numerical, zero is considered FALSE and anything else TRUE. Strings and empty values are ignored. If no logical values are provided, then the error #VALUE! is returned. This function is strict: if any argument is an error, the result will be the first such error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`OR`, `NOT`, `IF`.

`FALSE`
`FALSE` the value `FALSE`

    FALSE()

#### Description

`FALSE` returns the value `FALSE`.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TRUE`, `IF`.

`IF`
`IF` conditional expression

    IF(cond,trueval,falseval)

#### Arguments

cond: condition

trueval: value to use if condition is true

falseval: value to use if condition is false

#### Description

This function first evaluates the condition. If the result is true, it will then evaluate and return the second argument. Otherwise, it will evaluate and return the last argument.

#### See also

`AND`, `OR`, `XOR`, `NOT`, `IFERROR`.

`IFERROR`
`IFERROR` test for error

    IFERROR(x,y)

#### Arguments

x: value to test for error

y: alternate value

#### Description

This function returns the first value, unless that is an error, in which case it returns the second.

#### See also

`IF`, `ISERROR`.

`IFNA`
`IFNA` test for #NA! error

    IFNA(x,y)

#### Arguments

x: value to test for #NA! error

y: alternate value

#### Description

This function returns the first value, unless that is #NA!, in which case it returns the second.

#### See also

`IF`, `ISERROR`.

`NOT`
`NOT` logical negation

    NOT(b)

#### Arguments

b: logical value

#### Description

`NOT` calculates the logical negation of its argument.

#### Note

If the argument is numerical, zero is considered FALSE and anything else TRUE. Strings and empty values are ignored.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AND`, `OR`, `IF`.

`OR`
`OR` logical disjunction

    OR(b0,b1)

#### Arguments

b0: logical value

b1: logical value

#### Description

`OR` calculates the logical disjunction of its arguments b0,b1,...

#### Note

If an argument is numerical, zero is considered FALSE and anything else TRUE. Strings and empty values are ignored. If no logical values are provided, then the error #VALUE! is returned. This function is strict: if any argument is an error, the result will be the first such error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AND`, `XOR`, `NOT`, `IF`.

`TRUE`
`TRUE` the value `TRUE`

    TRUE()

#### Description

`TRUE` returns the value `TRUE`.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FALSE`, `IF`.

`XOR`
`XOR` logical exclusive disjunction

    XOR(b0,b1)

#### Arguments

b0: logical value

b1: logical value

#### Description

`XOR` calculates the logical exclusive disjunction of its arguments b0,b1,...

#### Note

If an argument is numerical, zero is considered FALSE and anything else TRUE. Strings and empty values are ignored. If no logical values are provided, then the error #VALUE! is returned. This function is strict: if any argument is an error, the result will be the first such error.

#### See also

`OR`, `AND`, `NOT`, `IF`.

## Lookup

`ADDRESS`
`ADDRESS` cell address as text

    ADDRESS(row_num,col_num,abs_num,a1,text)

#### Arguments

row_num: row number

col_num: column number

abs_num: 1 for an absolute, 2 for a row absolute and column relative, 3 for a row relative and column absolute, and 4 for a relative reference; defaults to 1

a1: if TRUE, an A1-style reference is provided, otherwise an R1C1-style reference; defaults to TRUE

text: name of the worksheet, defaults to no sheet

#### Note

If row_num or col_num is less than one, `ADDRESS` returns #VALUE! If abs_num is greater than 4 `ADDRESS` returns #VALUE!

#### See also

`COLUMNNUMBER`.

`AREAS`
`AREAS` number of areas in reference

    AREAS(reference)

#### Arguments

reference: range

#### See also

`ADDRESS`, `INDEX`, `INDIRECT`, `OFFSET`.

`ARRAY`
`ARRAY` vertical array of the arguments

    ARRAY(v)

#### Arguments

v: value

#### See also

`TRANSPOSE`.

`CHOOSE`
`CHOOSE` the (index+1)th argument

    CHOOSE(index,value1,value2)

#### Arguments

index: positive number

value1: first value

value2: second value

#### Description

`CHOOSE` returns its (index+1)th argument.

#### Note

index is truncated to an integer. If index < 1 or the truncated index > number of values, `CHOOSE` returns #VALUE!

#### See also

`IF`.

`COLUMN`
`COLUMN` vector of column numbers

    COLUMN(x)

#### Arguments

x: reference, defaults to the position of the current expression

#### Description

`COLUMN` function returns a Nx1 array containing the sequence of integers from the first column to the last column of x.

#### Note

If x is neither an array nor a reference nor a range, returns #VALUE!

#### See also

`COLUMNS`, `ROW`, `ROWS`.

`COLUMNNUMBER`
`COLUMNNUMBER` column number for the given column called name

    COLUMNNUMBER(name)

#### Arguments

name: column name such as "IV"

#### Note

If name is invalid, `COLUMNNUMBER` returns #VALUE!

#### See also

`ADDRESS`.

`COLUMNS`
`COLUMNS` number of columns in reference

    COLUMNS(reference)

#### Arguments

reference: array or area

#### Note

If reference is neither an array nor a reference nor a range, `COLUMNS` returns #VALUE!

#### See also

`COLUMN`, `ROW`, `ROWS`.

`HLOOKUP`
`HLOOKUP` search the first row of range for value

    HLOOKUP(value,range,row,approximate,as_index)

#### Arguments

value: search value

range: range to search

row: 1-based column offset indicating the return values

approximate: if false, an exact match of value must be found; defaults to TRUE

as_index: if true, the 0-based row offset is returned; defaults to FALSE

#### Description

`HLOOKUP` function finds the row in range that has a first cell similar to value. If approximate is not true it finds the row with an exact equality. If approximate is true, it finds the last row with first value less than or equal to value. If as_index is true the 0-based row offset is returned.

#### Note

If approximate is true, then the values must be sorted in order of ascending value. `HLOOKUP` returns #REF! if row falls outside range.

#### See also

`VLOOKUP`.

`HYPERLINK`
`HYPERLINK` second or first arguments

    HYPERLINK(link_location,label)

#### Arguments

link_location: string

label: string, optional

#### Description

`HYPERLINK` function currently returns its 2nd argument, or if that is omitted the 1st argument.

`INDEX`
`INDEX` reference to a cell in the given array

    INDEX(array,row,col,area)

#### Arguments

array: cell or inline array

row: desired row, defaults to 1

col: desired column, defaults to 1

area: from which area to select a cell, defaults to 1

#### Description

`INDEX` gives a reference to a cell in the given array. The cell is selected by row and col, which count the rows and columns in the array.

#### Note

If the reference falls outside the range of array, `INDEX` returns #REF!

`INDIRECT`
`INDIRECT` contents of the cell pointed to by the ref_text string

    INDIRECT(ref_text,format)

#### Arguments

ref_text: textual reference

format: if true, ref_text is given in A1-style, otherwise it is given in R1C1 style; defaults to true

#### Note

If ref_text is not a valid reference in the style determined by format, `INDIRECT` returns #REF!

#### See also

`AREAS`, `INDEX`, `CELL`.

`LOOKUP`
`LOOKUP` contents of vector2 at the corresponding location to value in vector1

    LOOKUP(value,vector1,vector2)

#### Arguments

value: value to look up

vector1: range to search:

vector2: range of return values

#### Description

If vector1 has more rows than columns, `LOOKUP` searches the first row of vector1, otherwise the first column. If vector2 is omitted the return value is taken from the last row or column of vector1.

#### Note

If `LOOKUP` can't find value it uses the largest value less than value. The data must be sorted. If value is smaller than the first value it returns #N/A. If the corresponding location does not exist in vector2, it returns #N/A.

#### See also

`VLOOKUP`, `HLOOKUP`.

`MATCH`
`MATCH` the index of seek in vector

    MATCH(seek,vector,type)

#### Arguments

seek: value to find

vector: n by 1 or 1 by n range to be searched

type: +1 (the default) to find the largest value ≤ seek, 0 to find the first value = seek, or-1 to find the smallest value ≥ seek

#### Description

`MATCH` searches vector for seek and returns the 1-based index.

#### Note

For type = -1 the data must be sorted in descending order; for type = +1 the data must be sorted in ascending order. If seek could not be found, #N/A is returned. If vector is neither n by 1 nor 1 by n, #N/A is returned.

#### See also

`LOOKUP`.

`OFFSET`
`OFFSET` an offset cell range

    OFFSET(range,row,col,height,width)

#### Arguments

range: reference or range

row: number of rows to offset range

col: number of columns to offset range

height: height of the offset range, defaults to height of range

width: width of the offset range, defaults to width of range

#### Description

`OFFSET` returns the cell range starting at offset (row,col) from range of height height and width width.

#### Note

If range is neither a reference nor a range, `OFFSET` returns #VALUE!

#### See also

`COLUMN`, `COLUMNS`, `ROWS`, `INDEX`, `INDIRECT`, `ADDRESS`.

`ROW`
`ROW` vector of row numbers

    ROW(x)

#### Arguments

x: reference, defaults to the position of the current expression

#### Description

`ROW` function returns a 1xN array containing the sequence of integers from the first row to the last row of x.

#### Note

If x is neither an array nor a reference nor a range, returns #VALUE!

#### See also

`COLUMN`, `COLUMNS`, `ROWS`.

`ROWS`
`ROWS` number of rows in reference

    ROWS(reference)

#### Arguments

reference: array, reference, or range

#### Note

If reference is neither an array nor a reference nor a range, `ROWS` returns #VALUE!

#### See also

`COLUMN`, `COLUMNS`, `ROW`.

`SHEET`
`SHEET` sheet number of reference

    SHEET(reference)

#### Arguments

reference: reference or literal sheet name, defaults to the current sheet

#### Note

If reference is neither a reference nor a literal sheet name, `SHEET` returns #VALUE!

#### See also

`SHEETS`, `ROW`, `COLUMNNUMBER`.

`SHEETS`
`SHEETS` number of sheets in reference

    SHEETS(reference)

#### Arguments

reference: array, reference, or range, defaults to the maximum range

#### Note

If reference is neither an array nor a reference nor a range, `SHEETS` returns #VALUE!

#### See also

`COLUMNS`, `ROWS`.

`SORT`
`SORT` sorted list of numbers as vertical array

    SORT(ref,order)

#### Arguments

ref: list of numbers

order: 0 (descending order) or 1 (ascending order); defaults to 0

#### Note

Strings, booleans, and empty cells are ignored.

#### See also

`ARRAY`.

`TRANSPOSE`
`TRANSPOSE` the transpose of matrix

    TRANSPOSE(matrix)

#### Arguments

matrix: range

#### See also

`MMULT`.

`VLOOKUP`
`VLOOKUP` search the first column of range for value

    VLOOKUP(value,range,column,approximate,as_index)

#### Arguments

value: search value

range: range to search

column: 1-based column offset indicating the return values

approximate: if false, an exact match of value must be found; defaults to TRUE

as_index: if true, the 0-based row offset is returned; defaults to FALSE

#### Description

`VLOOKUP` function finds the row in range that has a first cell similar to value. If approximate is not true it finds the row with an exact equality. If approximate is true, it finds the last row with first value less than or equal to value. If as_index is true the 0-based row offset is returned.

#### Note

If approximate is true, then the values must be sorted in order of ascending value. `VLOOKUP` returns #REF! if row falls outside range.

#### See also

`HLOOKUP`.

## Mathematics

`ABS`
`ABS` absolute value

    ABS(x)

#### Arguments

x: number

#### Description

`ABS` gives the absolute value of x, i.e. the non-negative number of the same magnitude as x.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CEIL`, `CEILING`, `FLOOR`, `INT`, `MOD`.

`ACOS`
`ACOS` the arc cosine of x

    ACOS(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COS`, `SIN`, `DEGREES`, `RADIANS`.

`ACOSH`
`ACOSH` the hyperbolic arc cosine of x

    ACOSH(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ACOS`, `ASINH`.

`ACOT`
`ACOT` inverse cotangent of x

    ACOT(x)

#### Arguments

x: value

#### See also

`COT`, `TAN`.

`ACOTH`
`ACOTH` the inverse hyperbolic cotangent of x

    ACOTH(x)

#### Arguments

x: number

#### See also

`COTH`, `TANH`.

`ARABIC`
`ARABIC` the Roman numeral roman as number

    ARABIC(roman)

#### Arguments

roman: Roman numeral

#### Description

Any Roman symbol to the left of a larger symbol (directly or indirectly) reduces the final value by the symbol amount, otherwise, it increases the final amount by the symbol's amount.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`ROMAN`.

`ASIN`
`ASIN` the arc sine of x

    ASIN(x)

#### Arguments

x: number

#### Description

`ASIN` calculates the arc sine of x; that is the value whose sine is x.

#### Note

If x falls outside the range -1 to 1, `ASIN` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SIN`, `COS`, `ASINH`, `DEGREES`, `RADIANS`.

`ASINH`
`ASINH` the inverse hyperbolic sine of x

    ASINH(x)

#### Arguments

x: number

#### Description

`ASINH` calculates the inverse hyperbolic sine of x; that is the value whose hyperbolic sine is x.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ASIN`, `ACOSH`, `SIN`, `COS`.

`ATAN`
`ATAN` the arc tangent of x

    ATAN(x)

#### Arguments

x: number

#### Description

`ATAN` calculates the arc tangent of x; that is the value whose tangent is x.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TAN`, `COS`, `SIN`, `DEGREES`, `RADIANS`.

`ATAN2`
`ATAN2` the arc tangent of the ratio of y and x

    ATAN2(y,x)

#### Arguments

y: y-coordinate

x: x-coordinate

#### Description

`ATAN2` calculates the direction from the origin to (x,y) as an angle in radians.

#### Note

The result will be between π and +π. The order of the arguments may be unexpected.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ATAN`, `ATANH`, `COS`, `SIN`.

`ATANH`
`ATANH` the inverse hyperbolic tangent of x

    ATANH(x)

#### Arguments

x: number

#### Description

`ATANH` calculates the inverse hyperbolic tangent of x; that is the value whose hyperbolic tangent is x.

#### Note

If the absolute value of x is greater than 1.0, `ATANH` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ATAN`, `COS`, `SIN`.

`AVERAGEIF`
`AVERAGEIF` average of the cells in @{actual range} for which the corresponding cells in the range meet the given criteria

    AVERAGEIF(range,criteria,actual_range)

#### Arguments

range: cell area

criteria: condition for a cell to be included

actual_range: cell area, defaults to range

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SUMIF`, `COUNTIF`.

`BETA`
`BETA` Euler beta function

    BETA(x,y)

#### Arguments

x: number

y: number

#### Description

`BETA` function returns the value of the Euler beta function extended to all real numbers except 0 and negative integers.

#### Note

If x, y, or (x + y) are non-positive integers, `BETA` returns #NUM!

#### See also

`BETALN`, `GAMMALN`.

`BETALN`
`BETALN` natural logarithm of the absolute value of the Euler beta function

    BETALN(x,y)

#### Arguments

x: number

y: number

#### Description

`BETALN` function returns the natural logarithm of the absolute value of the Euler beta function extended to all real numbers except 0 and negative integers.

#### Note

If x, y, or (x + y) are non-positive integers, `BETALN` returns #NUM!

#### See also

`BETA`, `GAMMALN`.

`CEIL`
`CEIL` smallest integer larger than or equal to x

    CEIL(x)

#### Arguments

x: number

#### Description

`CEIL`(x) is the smallest integer that is at least as large as x.

#### OpenDocument Format (ODF) Compatibility

This function is the OpenFormula function CEILING(x).

#### See also

`CEILING`, `FLOOR`, `ABS`, `INT`, `MOD`.

`CEILING`
`CEILING` nearest multiple of significance whose absolute value is at least ABS(x)

    CEILING(x,significance)

#### Arguments

x: number

significance: base multiple (defaults to 1 for x > 0 and -1 for x <0)

#### Description

`CEILING`(x,significance) is the nearest multiple of significance whose absolute value is at least ABS(x).

#### Note

If x or significance is non-numeric, `CEILING` returns a #VALUE! error. If x and significance have different signs, `CEILING` returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`CEILING`(x) is exported to ODF as `CEILING`(x,SIGN(x),1). `CEILING`(x,significance) is the OpenFormula function `CEILING`(x,significance,1).

#### See also

`CEIL`, `FLOOR`, `ABS`, `INT`, `MOD`.

`CHOLESKY`
`CHOLESKY` the Cholesky decomposition of the symmetric positive-definite matrix

    CHOLESKY(matrix)

#### Arguments

matrix: a symmetric positive definite matrix

#### Note

If the Cholesky-Banachiewicz algorithm applied to matrix fails, Cholesky returns #NUM! If matrix does not contain an equal number of columns and rows, `CHOLESKY` returns #VALUE!

#### See also

`MINVERSE`, `MMULT`, `MDETERM`.

`COMBIN`
`COMBIN` binomial coefficient

    COMBIN(n,k)

#### Arguments

n: non-negative integer

k: non-negative integer

#### Description

`COMBIN` returns the binomial coefficient "n choose k", the number of k-combinations of an n-element set without repetition.

#### Note

If n is less than k `COMBIN` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

`COMBINA`
`COMBINA` the number of k-combinations of an n-element set with repetition

    COMBINA(n,k)

#### Arguments

n: non-negative integer

k: non-negative integer

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`COMBIN`.

`COS`
`COS` the cosine of x

    COS(x)

#### Arguments

x: angle in radians

#### Description

This function is Excel compatible.

#### See also

`SIN`, `TAN`, `SINH`, `COSH`, `TANH`, `RADIANS`, `DEGREES`.

`COSH`
`COSH` the hyperbolic cosine of x

    COSH(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SIN`, `TAN`, `SINH`, `COSH`, `TANH`.

`COT`
`COT` the cotangent of x

    COT(x)

#### Arguments

x: number

#### See also

`TAN`, `ACOT`.

`COTH`
`COTH` the hyperbolic cotangent of x

    COTH(x)

#### Arguments

x: number

#### See also

`TANH`, `ACOTH`.

`COUNTIF`
`COUNTIF` count of the cells meeting the given criteria

    COUNTIF(range,criteria)

#### Arguments

range: cell area

criteria: condition for a cell to be counted

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COUNT`, `SUMIF`.

`CSC`
`CSC` the cosecant of x

    CSC(x)

#### Arguments

x: angle in radians

#### Microsoft Excel Compatibility

This function is not Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`SIN`, `COS`, `TAN`, `SEC`, `SINH`, `COSH`, `TANH`, `RADIANS`, `DEGREES`.

`CSCH`
`CSCH` the hyperbolic cosecant of x

    CSCH(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is not Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`SIN`, `COS`, `TAN`, `CSC`, `SEC`, `SINH`, `COSH`, `TANH`.

`DEGREES`
`DEGREES` equivalent degrees to x radians

    DEGREES(x)

#### Arguments

x: angle in radians

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`RADIANS`, `PI`.

`EIGEN`
`EIGEN` eigenvalues and eigenvectors of the symmetric matrix

    EIGEN(matrix)

#### Arguments

matrix: a symmetric matrix

#### Note

If matrix is not symmetric, `EIGEN` returns #NUM! If matrix does not contain an equal number of columns and rows, `EIGEN` returns #VALUE!

`EVEN`
`EVEN` x rounded away from 0 to the next even integer

    EVEN(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ODD`.

`EXP`
`EXP` e raised to the power of x

    EXP(x)

#### Arguments

x: number

#### Note

e is the base of the natural logarithm.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`LOG`, `LOG2`, `LOG10`.

`EXPM1`
`EXPM1` EXP(x)-1

    EXPM1(x)

#### Arguments

x: number

#### Note

This function has a higher resulting precision than evaluating EXP(x)-1.

#### See also

`EXP`, `LN1P`.

`FACT`
`FACT` the factorial of x, i.e. x!

    FACT(x)

#### Arguments

x: number

#### Note

The domain of this function has been extended using the GAMMA function.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`FACTDOUBLE`
`FACTDOUBLE` double factorial

    FACTDOUBLE(x)

#### Arguments

x: non-negative integer

#### Description

`FACTDOUBLE` function returns the double factorial x!!

#### Note

If x is not an integer, it is truncated. If x is negative, `FACTDOUBLE` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FACT`.

`FIB`
`FIB` Fibonacci numbers

    FIB(n)

#### Arguments

n: positive integer

#### Description

`FIB`(n) is the nth Fibonacci number.

#### Note

If n is not an integer, it is truncated. If it is negative or zero `FIB` returns #NUM!

`FLOOR`
`FLOOR` nearest multiple of significance whose absolute value is at most ABS(x)

    FLOOR(x,significance)

#### Arguments

x: number

significance: base multiple (defaults to 1 for x > 0 and -1 for x <0)

#### Description

`FLOOR`(x,significance) is the nearest multiple of significance whose absolute value is at most ABS(x)

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`FLOOR`(x) is exported to ODF as `FLOOR`(x,SIGN(x),1). `FLOOR`(x,significance) is the OpenFormula function `FLOOR`(x,significance,1).

#### See also

`CEIL`, `CEILING`, `ABS`, `INT`, `MOD`.

`G_PRODUCT`
`G_PRODUCT` product of all the values and cells referenced

    G_PRODUCT(x1,x2)

#### Arguments

x1: number

x2: number

#### Note

Empty cells are ignored and the empty product is 1.

#### See also

`SUM`, `COUNT`.

`GAMMA`
`GAMMA` the Gamma function

    GAMMA(x)

#### Arguments

x: number

#### See also

`GAMMALN`.

`GAMMALN`
`GAMMALN` natural logarithm of the Gamma function

    GAMMALN(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`GAMMA`.

`GCD`
`GCD` the greatest common divisor

    GCD(n0,n1)

#### Arguments

n0: positive integer

n1: positive integer

#### Description

`GCD` calculates the greatest common divisor of the given numbers n0,n1,..., the greatest integer that is a divisor of each argument.

#### Note

If any of the arguments is not an integer, it is truncated.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`LCM`.

`GD`
`GD` Gudermannian function

    GD(x)

#### Arguments

x: value

#### See also

`TAN`, `TANH`.

`HYPOT`
`HYPOT` the square root of the sum of the squares of the arguments

    HYPOT(n0,n1)

#### Arguments

n0: number

n1: number

#### See also

`MIN`, `MAX`.

`INT`
`INT` largest integer not larger than x

    INT(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CEIL`, `CEILING`, `FLOOR`, `ABS`, `MOD`.

`LCM`
`LCM` the least common multiple

    LCM(n0,n1)

#### Arguments

n0: positive integer

n1: positive integer

#### Description

`LCM` calculates the least common multiple of the given numbers n0,n1,..., the smallest integer that is a multiple of each argument.

#### Note

If any of the arguments is not an integer, it is truncated.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`GCD`.

`LN`
`LN` the natural logarithm of x

    LN(x)

#### Arguments

x: positive number

#### Note

If x ≤ 0, `LN` returns #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`EXP`, `LOG2`, `LOG10`.

`LN1P`
`LN1P` LN(1+x)

    LN1P(x)

#### Arguments

x: positive number

#### Description

`LN1P` calculates LN(1+x) but yielding a higher precision than evaluating LN(1+x).

#### Note

If x ≤ -1, LN returns #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`EXP`, `LN`, `EXPM1`.

`LOG`
`LOG` logarithm of x with base base

    LOG(x,base)

#### Arguments

x: positive number

base: base of the logarithm, defaults to 10

#### Note

base must be positive and not equal to 1. If x ≤ 0, `LOG` returns #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`LN`, `LOG2`, `LOG10`.

`LOG10`
`LOG10` the base-10 logarithm of x

    LOG10(x)

#### Arguments

x: positive number

#### Note

If x ≤ 0, `LOG10` returns #NUM!

#### See also

`EXP`, `LOG2`, `LOG`.

`LOG2`
`LOG2` the base-2 logarithm of x

    LOG2(x)

#### Arguments

x: positive number

#### Note

If x ≤ 0, `LOG2` returns #NUM!

#### See also

`EXP`, `LOG10`, `LOG`.

`MDETERM`
`MDETERM` the determinant of the matrix matrix

    MDETERM(matrix)

#### Arguments

matrix: a square matrix

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`MMULT`, `MINVERSE`.

`MINVERSE`
`MINVERSE` the inverse matrix of matrix

    MINVERSE(matrix)

#### Arguments

matrix: a square matrix

#### Note

If matrix is not invertible, `MINVERSE` returns #NUM! If matrix does not contain an equal number of columns and rows, `MINVERSE` returns #VALUE!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`MMULT`, `MDETERM`.

`MMULT`
`MMULT` the matrix product of mat1 and mat2

    MMULT(mat1,mat2)

#### Arguments

mat1: a matrix

mat2: a matrix

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TRANSPOSE`, `MINVERSE`.

`MOD`
`MOD` the remainder of x under division by n

    MOD(x,n)

#### Arguments

x: integer

n: integer

#### Description

`MOD` function returns the remainder when x is divided by n.

#### Note

If n is 0, `MOD` returns #DIV/0!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CEIL`, `CEILING`, `FLOOR`, `ABS`, `INT`, `ABS`.

`MROUND`
`MROUND` x rounded to a multiple of m

    MROUND(x,m)

#### Arguments

x: number

m: number

#### Note

If x and m have different sign, `MROUND` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ROUNDDOWN`, `ROUND`, `ROUNDUP`.

`MULTINOMIAL`
`MULTINOMIAL` multinomial coefficient (x1+⋯+xn) choose (x1,…,xn)

    MULTINOMIAL(x1,x2,xn)

#### Arguments

x1: first number

x2: second number

xn: nth number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COMBIN`, `SUM`.

`MUNIT`
`MUNIT` the n by n identity matrix

    MUNIT(n)

#### Arguments

n: size of the matrix

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`MMULT`, `MDETERM`, `MINVERSE`.

`ODD`
`ODD` x rounded away from 0 to the next odd integer

    ODD(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`EVEN`.

`PI`
`PI` the constant π

    PI()

#### Microsoft Excel Compatibility

This function is Excel compatible, but it returns π with a better precision.

#### See also

`SQRTPI`.

`POWER`
`POWER` the value of x raised to the power y

    POWER(x,y)

#### Arguments

x: number

y: number

#### Note

If both x and y equal 0, `POWER` returns #NUM! If x = 0 and y < 0, `POWER` returns #DIV/0! If x < 0 and y is not an integer, `POWER` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`EXP`.

`PRODUCT`
`PRODUCT` product of the given values

    PRODUCT(values)

#### Arguments

values: a list of values to multiply

#### Description

Product computes the product of all the values and cells referenced in the argument list.

#### Note

If all cells are empty, the result will be 0.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`SUM`, `COUNT`, `G_PRODUCT`.

`QUOTIENT`
`QUOTIENT` integer portion of a division

    QUOTIENT(numerator,denominator)

#### Arguments

numerator: integer

denominator: non-zero integer

#### Description

`QUOTIENT` yields the integer portion of the division numerator/denominator.

`QUOTIENT` (numerator,denominator)⨉denominator+MOD(numerator,denominator)=numerator

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`MOD`.

`RADIANS`
`RADIANS` the number of radians equivalent to x degrees

    RADIANS(x)

#### Arguments

x: angle in degrees

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`PI`, `DEGREES`.

`ROMAN`
`ROMAN` n as a roman numeral text

    ROMAN(n,type)

#### Arguments

n: non-negative integer

type: 0,1,2,3,or 4, defaults to 0

#### Description

`ROMAN` returns the arabic number n as a roman numeral text.

If type is 0 or it is omitted, `ROMAN` returns classic roman numbers.

Type 1 is more concise than classic type, type 2 is more concise than type 1, and type 3 is more concise than type 2. Type 4 is a simplified type.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`ROUND`
`ROUND` rounded x

    ROUND(x,d)

#### Arguments

x: number

d: integer, defaults to 0

#### Description

If d is greater than zero, x is rounded to the given number of digits.

If d is zero, x is rounded to the next integer.

If d is less than zero, x is rounded to the left of the decimal point

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ROUNDDOWN`, `ROUNDUP`.

`ROUNDDOWN`
`ROUNDDOWN` x rounded towards 0

    ROUNDDOWN(x,d)

#### Arguments

x: number

d: integer, defaults to 0

#### Description

If d is greater than zero, x is rounded toward 0 to the given number of digits.

If d is zero, x is rounded toward 0 to the next integer.

If d is less than zero, x is rounded toward 0 to the left of the decimal point

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ROUND`, `ROUNDUP`.

`ROUNDUP`
`ROUNDUP` x rounded away from 0

    ROUNDUP(x,d)

#### Arguments

x: number

d: integer, defaults to 0

#### Description

If d is greater than zero, x is rounded away from 0 to the given number of digits.

If d is zero, x is rounded away from 0 to the next integer.

If d is less than zero, x is rounded away from 0 to the left of the decimal point

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ROUND`, `ROUNDDOWN`, `INT`.

`SEC`
`SEC` Secant

    SEC(x)

#### Arguments

x: angle in radians

#### Microsoft Excel Compatibility

This function is not Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`SEC`(x) is exported to OpenFormula as 1/COS(x).

#### See also

`SIN`, `COS`, `TAN`, `CSC`, `SINH`, `COSH`, `TANH`, `RADIANS`, `DEGREES`.

`SECH`
`SECH` the hyperbolic secant of x

    SECH(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is not Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`SECH`(x) is exported to OpenFormula as 1/COSH(x).

#### See also

`SIN`, `COS`, `TAN`, `CSC`, `SEC`, `SINH`, `COSH`, `TANH`.

`SERIESSUM`
`SERIESSUM` sum of a power series at x

    SERIESSUM(x,n,m,coeff)

#### Arguments

x: number where to evaluate the power series

n: non-negative integer, exponent of the lowest term of the series

m: increment to each exponent

coeff: coefficients of the power series

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COUNT`, `SUM`.

`SIGN`
`SIGN` sign of x

    SIGN(x)

#### Arguments

x: number

#### Description

`SIGN` returns 1 if the x is positive and it returns -1 if x is negative.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`ABS`.

`SIN`
`SIN` the sine of x

    SIN(x)

#### Arguments

x: angle in radians

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COS`, `TAN`, `CSC`, `SEC`, `SINH`, `COSH`, `TANH`, `RADIANS`, `DEGREES`.

`SINH`
`SINH` the hyperbolic sine of x

    SINH(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SIN`, `COSH`, `ASINH`.

`SQRT`
`SQRT` square root of x

    SQRT(x)

#### Arguments

x: non-negative number

#### Note

If x is negative, `SQRT` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`POWER`.

`SQRTPI`
`SQRTPI` the square root of x times π

    SQRTPI(x)

#### Arguments

x: non-negative number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`PI`.

`SUM`
`SUM` sum of the given values

    SUM(values)

#### Arguments

values: a list of values to add

#### Description

`SUM` computes the sum of all the values and cells referenced in the argument list.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`AVERAGE`, `COUNT`.

`SUMA`
`SUMA` sum of all values and cells referenced

    SUMA(area0,area1)

#### Arguments

area0: first cell area

area1: second cell area

#### Description

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1).

#### See also

`AVERAGE`, `SUM`, `COUNT`.

`SUMIF`
`SUMIF` sum of the cells in actual_range for which the corresponding cells in the range meet the given criteria

    SUMIF(range,criteria,actual_range)

#### Arguments

range: cell area

criteria: condition for a cell to be summed

actual_range: cell area, defaults to range

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SUM`, `COUNTIF`.

`SUMPRODUCT`
`SUMPRODUCT` multiplies components and adds the results

    SUMPRODUCT()

#### Description

Multiplies corresponding data entries in the given arrays or ranges, and then returns the sum of those products.

#### Note

If an entry is not numeric, the value zero is used instead. If arrays or range arguments do not have the same dimensions, return #VALUE! error. SUMPRODUCTs arguments are arrays or ranges. Attempting to use A1:A5>0 will not work, implicit intersection will kick in. Instead use --(A1:A5>0)

#### See also

`SUM`, `PRODUCT`, `G_PRODUCT`.

`SUMSQ`
`SUMSQ` sum of the squares of all values and cells referenced

    SUMSQ(area0,area1)

#### Arguments

area0: first cell area

area1: second cell area

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SUM`, `COUNT`.

`SUMX2MY2`
`SUMX2MY2` sum of the difference of squares

    SUMX2MY2(array0,array1)

#### Arguments

array0: first cell area

array1: second cell area

#### Description

`SUMX2MY2` function returns the sum of the difference of squares of corresponding values in two arrays. The equation of `SUMX2MY2` is SUM(x^2-y^2).

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SUMSQ`, `SUMX2PY2`.

`SUMX2PY2`
`SUMX2PY2` sum of the sum of squares

    SUMX2PY2(array0,array1)

#### Arguments

array0: first cell area

array1: second cell area

#### Description

`SUMX2PY2` function returns the sum of the sum of squares of corresponding values in two arrays. The equation of `SUMX2PY2` is SUM(x^2+y^2).

#### Note

If array0 and array1 have different number of data points, `SUMX2PY2` returns #N/A.

Strings and empty cells are simply ignored.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SUMSQ`, `SUMX2MY2`.

`SUMXMY2`
`SUMXMY2` sum of the squares of differences

    SUMXMY2(array0,array1)

#### Arguments

array0: first cell area

array1: second cell area

#### Description

`SUMXMY2` function returns the sum of the squares of the differences of corresponding values in two arrays. The equation of `SUMXMY2` is SUM((x-y)^2).

#### Note

If array0 and array1 have different number of data points, `SUMXMY2` returns #N/A.

Strings and empty cells are simply ignored.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SUMSQ`, `SUMX2MY2`, `SUMX2PY2`.

`TAN`
`TAN` the tangent of x

    TAN(x)

#### Arguments

x: angle in radians

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TANH`, `COS`, `COSH`, `SIN`, `SINH`, `DEGREES`, `RADIANS`.

`TANH`
`TANH` the hyperbolic tangent of x

    TANH(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TAN`, `SIN`, `SINH`, `COS`, `COSH`.

`TRUNC`
`TRUNC` x truncated to d digits

    TRUNC(x,d)

#### Arguments

x: number

d: non-negative integer, defaults to 0

#### Note

If d is omitted or negative then it defaults to zero. If it is not an integer then it is truncated to an integer.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`INT`.

## Number Theory

`ISPRIME`
`ISPRIME` whether n is prime

    ISPRIME(n)

#### Arguments

n: positive integer

#### Description

`ISPRIME` returns TRUE if n is prime and FALSE otherwise.

#### See also

`NT_D`, `NT_SIGMA`.

`ITHPRIME`
`ITHPRIME` ith prime

    ITHPRIME(i)

#### Arguments

i: positive integer

#### Description

`ITHPRIME` finds the ith prime.

#### See also

`NT_D`, `NT_SIGMA`.

`NT_D`
`NT_D` number of divisors

    NT_D(n)

#### Arguments

n: positive integer

#### Description

`NT_D` calculates the number of divisors of n.

#### See also

`ITHPRIME`, `NT_PHI`, `NT_SIGMA`.

`NT_MU`
`NT_MU` Möbius mu function

    NT_MU(n)

#### Arguments

n: positive integer

#### Description

`NT_MU` function (Möbius mu function) returns 0 if n is divisible by the square of a prime. Otherwise, if n has an odd number of different prime factors, `NT_MU` returns -1, and if n has an even number of different prime factors, it returns 1. If n = 1, `NT_MU` returns 1.

#### See also

`ITHPRIME`, `NT_PHI`, `NT_SIGMA`, `NT_D`.

`NT_PHI`
`NT_PHI` Euler's totient function

    NT_PHI(n)

#### Arguments

n: positive integer

#### Note

Euler's totient function gives the number of integers less than or equal to n that are relatively prime (coprime) to n.

#### See also

`NT_D`, `ITHPRIME`, `NT_SIGMA`.

`NT_PI`
`NT_PI` number of primes upto n

    NT_PI(n)

#### Arguments

n: positive integer

#### Description

`NT_PI` returns the number of primes less than or equal to n.

#### See also

`ITHPRIME`, `NT_PHI`, `NT_D`, `NT_SIGMA`.

`NT_SIGMA`
`NT_SIGMA` sigma function

    NT_SIGMA(n)

#### Arguments

n: positive integer

#### Description

`NT_SIGMA` calculates the sum of the divisors of n.

#### See also

`NT_D`, `ITHPRIME`, `NT_PHI`.

`PFACTOR`
`PFACTOR` smallest prime factor

    PFACTOR(n)

#### Arguments

n: positive integer

#### Description

`PFACTOR` finds the smallest prime factor of its argument.

#### Note

The argument n must be at least 2. Otherwise a #VALUE! error is returned.

#### See also

`ITHPRIME`.

## Random Numbers

`RAND`
`RAND` a random number between zero and one

    RAND()

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`RANDBETWEEN`.

`RANDBERNOULLI`
`RANDBERNOULLI` random variate from a Bernoulli distribution

    RANDBERNOULLI(p)

#### Arguments

p: probability of success

#### Note

If p < 0 or p > 1 `RANDBERNOULLI` returns #NUM!

#### See also

`RAND`, `RANDBETWEEN`.

`RANDBETA`
`RANDBETA` random variate from a Beta distribution

    RANDBETA(a,b)

#### Arguments

a: parameter of the Beta distribution

b: parameter of the Beta distribution

#### See also

`RAND`, `RANDGAMMA`.

`RANDBETWEEN`
`RANDBETWEEN` a random integer number between and including bottom and top

    RANDBETWEEN(bottom,top)

#### Arguments

bottom: lower limit

top: upper limit

#### Note

If bottom > top, `RANDBETWEEN` returns #NUM!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`RAND`, `RANDUNIFORM`.

`RANDBINOM`
`RANDBINOM` random variate from a binomial distribution

    RANDBINOM(p,n)

#### Arguments

p: probability of success in a single trial

n: number of trials

#### Note

If p < 0 or p > 1 `RANDBINOM` returns #NUM! If n < 0 `RANDBINOM` returns #NUM!

#### See also

`RAND`, `RANDBETWEEN`.

`RANDCAUCHY`
`RANDCAUCHY` random variate from a Cauchy or Lorentz distribution

    RANDCAUCHY(a)

#### Arguments

a: scale parameter of the distribution

#### Note

If a < 0 `RANDCAUCHY` returns #NUM!

#### See also

`RAND`.

`RANDCHISQ`
`RANDCHISQ` random variate from a Chi-square distribution

    RANDCHISQ(df)

#### Arguments

df: degrees of freedom

#### See also

`RAND`, `RANDGAMMA`.

`RANDDISCRETE`
`RANDDISCRETE` random variate from a finite discrete distribution

    RANDDISCRETE(val_range,prob_range)

#### Arguments

val_range: possible values of the random variable

prob_range: probabilities of the corresponding values in val_range, defaults to equal probabilities

#### Description

`RANDDISCRETE` returns one of the values in the val_range. The probabilities for each value are given in the prob_range.

#### Note

If the sum of all values in prob_range is not one, `RANDDISCRETE` returns #NUM! If val_range and prob_range are not the same size, `RANDDISCRETE` returns #NUM! If val_range or prob_range is not a range, `RANDDISCRETE` returns #VALUE!

#### See also

`RANDBETWEEN`, `RAND`.

`RANDEXP`
`RANDEXP` random variate from an exponential distribution

    RANDEXP(b)

#### Arguments

b: parameter of the exponential distribution

#### See also

`RAND`, `RANDBETWEEN`.

`RANDEXPPOW`
`RANDEXPPOW` random variate from an exponential power distribution

    RANDEXPPOW(a,b)

#### Arguments

a: scale parameter of the exponential power distribution

b: exponent of the exponential power distribution

#### Description

For b = 1 the exponential power distribution reduces to the Laplace distribution.

For b = 2 the exponential power distribution reduces to the normal distribution with σ = a/sqrt(2)

#### See also

`RAND`.

`RANDFDIST`
`RANDFDIST` random variate from an F distribution

    RANDFDIST(df1,df2)

#### Arguments

df1: numerator degrees of freedom

df2: denominator degrees of freedom

#### See also

`RAND`, `RANDGAMMA`.

`RANDGAMMA`
`RANDGAMMA` random variate from a Gamma distribution

    RANDGAMMA(a,b)

#### Arguments

a: parameter of the Gamma distribution

b: parameter of the Gamma distribution

#### Note

If a ≤ 0, `RANDGAMMA` returns #NUM!

#### See also

`RAND`.

`RANDGEOM`
`RANDGEOM` random variate from a geometric distribution

    RANDGEOM(p)

#### Arguments

p: probability of success in a single trial

#### Note

If p < 0 or p > 1 `RANDGEOM` returns #NUM!

#### See also

`RAND`.

`RANDGUMBEL`
`RANDGUMBEL` random variate from a Gumbel distribution

    RANDGUMBEL(a,b,type)

#### Arguments

a: parameter of the Gumbel distribution

b: parameter of the Gumbel distribution

type: type of the Gumbel distribution, defaults to 1

#### Note

If type is neither 1 nor 2, `RANDGUMBEL` returns #NUM!

#### See also

`RAND`.

`RANDHYPERG`
`RANDHYPERG` random variate from a hypergeometric distribution

    RANDHYPERG(n1,n2,t)

#### Arguments

n1: number of objects of type 1

n2: number of objects of type 2

t: total number of objects selected

#### See also

`RAND`.

`RANDLANDAU`
`RANDLANDAU` random variate from the Landau distribution

    RANDLANDAU()

#### See also

`RAND`.

`RANDLAPLACE`
`RANDLAPLACE` random variate from a Laplace distribution

    RANDLAPLACE(a)

#### Arguments

a: parameter of the Laplace distribution

#### See also

`RAND`.

`RANDLEVY`
`RANDLEVY` random variate from a Lévy distribution

    RANDLEVY(c,α,β)

#### Arguments

c: parameter of the Lévy distribution

@{α}: parameter of the Lévy distribution

@{β}: parameter of the Lévy distribution, defaults to 0

#### Description

For @{α} = 1, @{β}=0, the Lévy distribution reduces to the Cauchy (or Lorentzian) distribution.

For @{α} = 2, @{β}=0, the Lévy distribution reduces to the normal distribution.

#### Note

If @{α} ≤ 0 or @{α} > 2, `RANDLEVY` returns #NUM! If @{β} < -1 or @{β} > 1, `RANDLEVY` returns #NUM!

#### See also

`RAND`.

`RANDLOG`
`RANDLOG` random variate from a logarithmic distribution

    RANDLOG(p)

#### Arguments

p: probability

#### Note

If p < 0 or p > 1 `RANDLOG` returns #NUM!

#### See also

`RAND`.

`RANDLOGISTIC`
`RANDLOGISTIC` random variate from a logistic distribution

    RANDLOGISTIC(a)

#### Arguments

a: parameter of the logistic distribution

#### See also

`RAND`.

`RANDLOGNORM`
`RANDLOGNORM` random variate from a lognormal distribution

    RANDLOGNORM(ζ,σ)

#### Arguments

@{ζ}: parameter of the lognormal distribution

@{σ}: standard deviation of the distribution

#### Note

If @{σ} < 0, `RANDLOGNORM` returns #NUM!

#### See also

`RAND`.

`RANDNEGBINOM`
`RANDNEGBINOM` random variate from a negative binomial distribution

    RANDNEGBINOM(p,n)

#### Arguments

p: probability of success in a single trial

n: number of failures

#### Note

If p < 0 or p > 1 `RANDNEGBINOM` returns #NUM! If n < 1 `RANDNEGBINOM` returns #NUM!

#### See also

`RAND`, `RANDBETWEEN`.

`RANDNORM`
`RANDNORM` random variate from a normal distribution

    RANDNORM(μ,σ)

#### Arguments

@{μ}: mean of the distribution

@{σ}: standard deviation of the distribution

#### Note

If @{σ} < 0, `RANDNORM` returns #NUM!

#### See also

`RAND`.

`RANDNORMTAIL`
`RANDNORMTAIL` random variate from the upper tail of a normal distribution with mean 0

    RANDNORMTAIL(a,σ)

#### Arguments

a: lower limit of the tail

@{σ}: standard deviation of the normal distribution

#### Note

The method is based on Marsaglia's famous rectangle-wedge-tail algorithm (Ann Math Stat 32, 894-899 (1961)), with this aspect explained in Knuth, v2, 3rd ed, p139, 586 (exercise 11).

#### See also

`RAND`.

`RANDPARETO`
`RANDPARETO` random variate from a Pareto distribution

    RANDPARETO(a,b)

#### Arguments

a: parameter of the Pareto distribution

b: parameter of the Pareto distribution

#### See also

`RAND`.

`RANDPOISSON`
`RANDPOISSON` random variate from a Poisson distribution

    RANDPOISSON(λ)

#### Arguments

@{λ}: parameter of the Poisson distribution

#### Note

If @{λ} < 0 `RANDPOISSON` returns #NUM!

#### See also

`RAND`, `RANDBETWEEN`.

`RANDRAYLEIGH`
`RANDRAYLEIGH` random variate from a Rayleigh distribution

    RANDRAYLEIGH(σ)

#### Arguments

@{σ}: scale parameter of the Rayleigh distribution

#### See also

`RAND`.

`RANDRAYLEIGHTAIL`
`RANDRAYLEIGHTAIL` random variate from the tail of a Rayleigh distribution

    RANDRAYLEIGHTAIL(a,σ)

#### Arguments

a: lower limit of the tail

@{σ}: scale parameter of the Rayleigh distribution

#### See also

`RAND`, `RANDRAYLEIGH`.

`RANDSNORM`
`RANDSNORM` random variate from a skew normal distribution

    RANDSNORM(a,μ,σ)

#### Arguments

a: amount of skew, defaults to 0

@{μ}: mean of the underlying normal distribution, defaults to 0

@{σ}: standard deviation of the underlying normal distribution, defaults to 1

#### Note

If @{σ} < 0, `RANDSNORM` returns #NUM!

#### See also

`RANDNORM`.

`RANDSTDIST`
`RANDSTDIST` random variate from a skew t distribution

    RANDSTDIST(df,a)

#### Arguments

df: degrees of freedom

a: amount of skew, defaults to 0

#### See also

`RANDTDIST`.

`RANDTDIST`
`RANDTDIST` random variate from a Student t distribution

    RANDTDIST(df)

#### Arguments

df: degrees of freedom

#### See also

`RAND`.

`RANDUNIFORM`
`RANDUNIFORM` random variate from the uniform distribution from a to b

    RANDUNIFORM(a,b)

#### Arguments

a: lower limit of the uniform distribution

b: upper limit of the uniform distribution

#### Note

If a > b `RANDUNIFORM` returns #NUM!

#### See also

`RANDBETWEEN`, `RAND`.

`RANDWEIBULL`
`RANDWEIBULL` random variate from a Weibull distribution

    RANDWEIBULL(a,b)

#### Arguments

a: parameter of the Weibull distribution

b: parameter of the Weibull distribution

#### See also

`RAND`.

`SIMTABLE`
`SIMTABLE` one of the values in the given argument list depending on the round number of the simulation tool

    SIMTABLE(d1,d2)

#### Arguments

d1: first value

d2: second value

#### Description

`SIMTABLE` returns one of the values in the given argument list depending on the round number of the simulation tool. When the simulation tool is not activated, `SIMTABLE` returns d1.

With the simulation tool and the `SIMTABLE` function you can test given decision variables. Each `SIMTABLE` function contains the possible values of a simulation variable. In most valid simulation models you should have the same number of values dN for all decision variables. If the simulation is run more rounds than there are values defined, `SIMTABLE` returns #N/A! error (e.g. if A1 contains `=`SIMTABLE`(1)' and A2 `=`SIMTABLE`(1,2)', A1 yields #N/A! error on the second round).

The successive use of the simulation tool also requires that you give to the tool at least one input variable having RAND() or any other RAND<distribution name>() function in it. On each round, the simulation tool iterates for the given number of rounds over all the input variables to reevaluate them. On each iteration, the values of the output variables are stored, and when the round is completed, descriptive statistical information is created according to the values.

## Statistics

`ADTEST`
`ADTEST` Anderson-Darling Test of Normality

    ADTEST(x)

#### Arguments

x: array of sample values

#### Description

This function returns an array with the first row giving the p-value of the Anderson-Darling Test, the second row the test statistic of the test, and the third the number of observations in the sample.

#### Note

If there are less than 8 sample values, `ADTEST` returns #VALUE!

#### See also

`CHITEST`, `CVMTEST`, `LKSTEST`, `SFTEST`.

`AVEDEV`
`AVEDEV` average of the absolute deviations of a data set

    AVEDEV(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`STDEV`.

`AVERAGE`
`AVERAGE` average of all the numeric values and cells

    AVERAGE(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`SUM`, `COUNT`.

`AVERAGEA`
`AVERAGEA` average of all the values and cells

    AVERAGEA(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`.

`BERNOULLI`
`BERNOULLI` probability mass function of a Bernoulli distribution

    BERNOULLI(k,p)

#### Arguments

k: integer

p: probability of success

#### Note

If k != 0 and k != 1 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error.

#### See also

`RANDBERNOULLI`.

`BETADIST`
`BETADIST` cumulative distribution function of the beta distribution

    BETADIST(x,alpha,beta,a,b)

#### Arguments

x: number

alpha: scale parameter

beta: scale parameter

a: optional lower bound, defaults to 0

b: optional upper bound, defaults to 1

#### Note

If x < a or x > b this function returns a #NUM! error. If alpha <= 0 or beta <= 0, this function returns a #NUM! error. If a >= b this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BETAINV`.

`BETAINV`
`BETAINV` inverse of the cumulative distribution function of the beta distribution

    BETAINV(p,alpha,beta,a,b)

#### Arguments

p: probability

alpha: scale parameter

beta: scale parameter

a: optional lower bound, defaults to 0

b: optional upper bound, defaults to 1

#### Note

If p < 0 or p > 1 this function returns a #NUM! error. If alpha <= 0 or beta <= 0, this function returns a #NUM! error. If a >= b this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BETADIST`.

`BINOM.DIST.RANGE`
`BINOM.DIST.RANGE` probability of the binomial distribution over an interval

    BINOM.DIST.RANGE(trials,p,start,end)

#### Arguments

trials: number of trials

p: probability of success in each trial

start: start of the interval

end: end of the interval, defaults to start

#### Note

If start, end or trials are non-integer they are truncated. If trials < 0 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error. If start > end this function returns 0.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`BINOMDIST`, `R.PBINOM`.

`BINOMDIST`
`BINOMDIST` probability mass of cumulative distribution function of the binomial distribution

    BINOMDIST(n,trials,p,cumulative)

#### Arguments

n: number of successes

trials: number of trials

p: probability of success in each trial

cumulative: whether to evaluate the mass function or the cumulative distribution function

#### Note

If n or trials are non-integer they are truncated. If n < 0 or trials < 0 this function returns a #NUM! error. If n > trials this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`POISSON`.

`CAUCHY`
`CAUCHY` probability density or cumulative distribution function of the Cauchy, Lorentz or Breit-Wigner distribution

    CAUCHY(x,a,cumulative)

#### Arguments

x: number

a: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

#### Note

If a < 0 this function returns a #NUM! error. If cumulative is neither TRUE nor FALSE this function returns a #VALUE! error.

#### See also

`RANDCAUCHY`.

`CHIDIST`
`CHIDIST` survival function of the chi-squared distribution

    CHIDIST(x,dof)

#### Arguments

x: number

dof: number of degrees of freedom

#### Description

The survival function is 1 minus the cumulative distribution function.

#### Note

If dof is non-integer it is truncated. If dof < 1 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`CHIDIST`(x,dof) is the OpenFormula function LEGACY.`CHIDIST`(x,dof).

#### See also

`CHIINV`, `CHITEST`.

`CHIINV`
`CHIINV` inverse of the survival function of the chi-squared distribution

    CHIINV(p,dof)

#### Arguments

p: probability

dof: number of degrees of freedom

#### Description

The survival function is 1 minus the cumulative distribution function.

#### Note

If p < 0 or p > 1 or dof < 1 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`CHIINV`(p,dof) is the OpenFormula function LEGACY.CHIDIST(p,dof).

#### See also

`CHIDIST`, `CHITEST`.

`CHITEST`
`CHITEST` p value of the Goodness of Fit Test

    CHITEST(actual_range,theoretical_range)

#### Arguments

actual_range: observed data

theoretical_range: expected values

#### Note

If the actual range is not an n by 1 or 1 by n range, but an n by m range, then `CHITEST` uses (n-1) times (m-1) as degrees of freedom. This is useful if the expected values were calculated from the observed value in a test of independence or test of homogeneity.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`CHITEST` is the OpenFormula function LEGACY.`CHITEST`.

#### See also

`CHIDIST`, `CHIINV`.

`CONFIDENCE`
`CONFIDENCE` margin of error of a confidence interval for the population mean

    CONFIDENCE(alpha,stddev,size)

#### Arguments

alpha: significance level

stddev: population standard deviation

size: sample size

#### Note

This function requires the usually unknown population standard deviation. If size is non-integer it is truncated. If size < 0 this function returns a #NUM! error. If size is 0 this function returns a #DIV/0! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`.

`CORREL`
`CORREL` Pearson correlation coefficient of two data sets

    CORREL(array1,array2)

#### Arguments

array1: first data set

array2: second data set

#### Description

Strings and empty cells are simply ignored.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COVAR`, `FISHER`, `FISHERINV`.

`COUNT`
`COUNT` total number of integer or floating point arguments passed

    COUNT(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`.

`COUNTA`
`COUNTA` number of arguments passed not including empty cells

    COUNTA(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `COUNT`, `DCOUNT`, `DCOUNTA`, `PRODUCT`, `SUM`.

`COVAR`
`COVAR` covariance of two data sets

    COVAR(array1,array2)

#### Arguments

array1: first data set

array2: set data set

#### Description

Strings and empty cells are simply ignored.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CORREL`, `FISHER`, `FISHERINV`.

`CRITBINOM`
`CRITBINOM` right-tailed critical value of the binomial distribution

    CRITBINOM(trials,p,alpha)

#### Arguments

trials: number of trials

p: probability of success in each trial

alpha: significance level (area of the tail)

#### Note

If trials is a non-integer it is truncated. If trials < 0 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error. If alpha < 0 or alpha > 1 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BINOMDIST`.

`CRONBACH`
`CRONBACH` Cronbach's alpha

    CRONBACH(ref1,ref2)

#### Arguments

ref1: first data set

ref2: second data set

#### See also

`VAR`.

`CVMTEST`
`CVMTEST` Cramér-von Mises Test of Normality

    CVMTEST(x)

#### Arguments

x: array of sample values

#### Description

This function returns an array with the first row giving the p-value of the Cramér-von Mises Test, the second row the test statistic of the test, and the third the number of observations in the sample.

#### Note

If there are less than 8 sample values, `CVMTEST` returns #VALUE!

#### See also

`CHITEST`, `ADTEST`, `LKSTEST`, `SFTEST`.

`DEVSQ`
`DEVSQ` sum of squares of deviations of a data set

    DEVSQ(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Strings and empty cells are simply ignored.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`STDEV`.

`EXPONDIST`
`EXPONDIST` probability density or cumulative distribution function of the exponential distribution

    EXPONDIST(x,y,cumulative)

#### Arguments

x: number

y: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

#### Description

If cumulative is false it will return: y * exp (-y*x),otherwise it will return 1 - exp (-y*x).

#### Note

If x < 0 or y <= 0 this will return an error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`POISSON`.

`EXPPOWDIST`
`EXPPOWDIST` the probability density function of the Exponential Power distribution

    EXPPOWDIST(x,a,b)

#### Arguments

x: number

a: scale parameter

b: scale parameter

#### Description

This distribution has been recommended for lifetime analysis when a U-shaped hazard function is desired. This corresponds to rapid failure once the product starts to wear out after a period of steady or even improving reliability.

#### See also

`RANDEXPPOW`.

`FDIST`
`FDIST` survival function of the F distribution

    FDIST(x,dof_of_num,dof_of_denom)

#### Arguments

x: number

dof_of_num: numerator degrees of freedom

dof_of_denom: denominator degrees of freedom

#### Description

The survival function is 1 minus the cumulative distribution function.

#### Note

If x < 0 this function returns a #NUM! error. If dof_of_num < 1 or dof_of_denom < 1, this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`FDIST` is the OpenFormula function LEGACY.`FDIST`.

#### See also

`FINV`.

`FINV`
`FINV` inverse of the survival function of the F distribution

    FINV(p,dof_of_num,dof_of_denom)

#### Arguments

p: probability

dof_of_num: numerator degrees of freedom

dof_of_denom: denominator degrees of freedom

#### Description

The survival function is 1 minus the cumulative distribution function.

#### Note

If p < 0 or p > 1 this function returns a #NUM! error. If dof_of_num < 1 or dof_of_denom < 1 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`FINV` is the OpenFormula function LEGACY.`FINV`.

#### See also

`FDIST`.

`FISHER`
`FISHER` Fisher transformation

    FISHER(x)

#### Arguments

x: number

#### Note

If x is not a number, this function returns a #VALUE! error. If x <= -1 or x >= 1, this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FISHERINV`, `ATANH`.

`FISHERINV`
`FISHERINV` inverse of the Fisher transformation

    FISHERINV(x)

#### Arguments

x: number

#### Note

If x is a non-number this function returns a #VALUE! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FISHER`, `TANH`.

`FORECAST`
`FORECAST` estimates a future value according to existing values using simple linear regression

    FORECAST(x,known_ys,known_xs)

#### Arguments

x: x-value whose matching y-value should be forecast

known_ys: known y-values

known_xs: known x-values

#### Description

This function estimates a future value according to existing values using simple linear regression.

#### Note

If known_xs or known_ys contains no data entries or different number of data entries, this function returns a #N/A error. If the variance of the known_xs is zero, this function returns a #DIV/0 error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`INTERCEPT`, `TREND`.

`FREQUENCY`
`FREQUENCY` frequency table

    FREQUENCY(data_array,bins_array)

#### Arguments

data_array: data values

bins_array: array of cutoff values

#### Description

The results are given as an array.

If the bins_array is empty, this function returns the number of data points in data_array.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`FTEST`
`FTEST` p-value for the two-tailed hypothesis test comparing the variances of two populations

    FTEST(array1,array2)

#### Arguments

array1: sample from the first population

array2: sample from the second population

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FDIST`, `FINV`.

`GAMMADIST`
`GAMMADIST` probability density or cumulative distribution function of the gamma distribution

    GAMMADIST(x,alpha,beta,cumulative)

#### Arguments

x: number

alpha: scale parameter

beta: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

#### Note

If x < 0 this function returns a #NUM! error. If alpha <= 0 or beta <= 0, this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`GAMMAINV`.

`GAMMAINV`
`GAMMAINV` inverse of the cumulative gamma distribution

    GAMMAINV(p,alpha,beta)

#### Arguments

p: probability

alpha: scale parameter

beta: scale parameter

#### Note

If p < 0 or p > 1 this function returns a #NUM! error. If alpha <= 0 or beta <= 0 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`GAMMADIST`.

`GEOMDIST`
`GEOMDIST` probability mass or cumulative distribution function of the hypergeometric distribution

    GEOMDIST(k,p,cumulative)

#### Arguments

k: number of trials

p: probability of success in any trial

cumulative: whether to evaluate the mass function or the cumulative distribution function

#### Note

If k < 0 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error. If cumulative is neither TRUE nor FALSE this function returns a #VALUE! error.

#### See also

`RANDGEOM`.

`GEOMEAN`
`GEOMEAN` geometric mean

    GEOMEAN(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

The geometric mean is equal to the Nth root of the product of the N values.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `HARMEAN`, `MEDIAN`, `MODE`, `TRIMMEAN`.

`GROWTH`
`GROWTH` exponential growth prediction

    GROWTH(known_ys,known_xs,new_xs,affine)

#### Arguments

known_ys: known y-values

known_xs: known x-values; defaults to the array {1, 2, 3, …}

new_xs: x-values for which to estimate the y-values; defaults to known_xs

affine: if true, the model contains a constant term, defaults to true

#### Description

`GROWTH` function applies the “least squares” method to fit an exponential curve to your data and predicts the exponential growth by using this curve.

`GROWTH` returns an array having one column and a row for each data point in new_xs.

#### Note

If known_ys and known_xs have unequal number of data points, this function returns a #NUM! error.

#### See also

`LOGEST`, `GROWTH`, `TREND`.

`HARMEAN`
`HARMEAN` harmonic mean

    HARMEAN(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

The harmonic mean of N data points is N divided by the sum of the reciprocals of the data points).

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `GEOMEAN`, `MEDIAN`, `MODE`, `TRIMMEAN`.

`HYPGEOMDIST`
`HYPGEOMDIST` probability mass or cumulative distribution function of the hypergeometric distribution

    HYPGEOMDIST(x,n,M,N,cumulative)

#### Arguments

x: number of successes

n: sample size

M: number of possible successes in the population

N: population size

cumulative: whether to evaluate the mass function or the cumulative distribution function

#### Note

If x,n,M or N is a non-integer it is truncated. If x,n,M or N < 0 this function returns a #NUM! error. If x > M or n > N this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BINOMDIST`, `POISSON`.

`INTERCEPT`
`INTERCEPT` the intercept of a linear regression line

    INTERCEPT(known_ys,known_xs)

#### Arguments

known_ys: known y-values

known_xs: known x-values

#### Note

If known_xs or known_ys contains no data entries or different number of data entries, this function returns a #N/A error. If the variance of the known_xs is zero, this function returns #DIV/0 error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FORECAST`, `TREND`.

`KURT`
`KURT` unbiased estimate of the kurtosis of a data set

    KURT(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Strings and empty cells are simply ignored.

#### Note

This is only meaningful if the underlying distribution really has a fourth moment. The kurtosis is offset by three such that a normal distribution will have zero kurtosis. If fewer than four numbers are given or all of them are equal this function returns a #DIV/0! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `VAR`, `SKEW`, `KURTP`.

`KURTP`
`KURTP` population kurtosis of a data set

    KURTP(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Strings and empty cells are simply ignored.

#### Note

If fewer than two numbers are given or all of them are equal this function returns a #DIV/0! error.

#### See also

`AVERAGE`, `VARP`, `SKEWP`, `KURT`.

`LANDAU`
`LANDAU` approximate probability density function of the Landau distribution

    LANDAU(x)

#### Arguments

x: number

#### See also

`RANDLANDAU`.

`LAPLACE`
`LAPLACE` probability density function of the Laplace distribution

    LAPLACE(x,a)

#### Arguments

x: number

a: mean

#### See also

`RANDLAPLACE`.

`LARGE`
`LARGE` k-th largest value in a data set

    LARGE(data,k)

#### Arguments

data: data set

k: which value to find

#### Note

If data set is empty this function returns a #NUM! error. If k <= 0 or k is greater than the number of data items given this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`PERCENTILE`, `PERCENTRANK`, `QUARTILE`, `SMALL`.

`LINEST`
`LINEST` multiple linear regression coefficients and statistics

    LINEST(known_ys,known_xs,affine,stats)

#### Arguments

known_ys: vector of values of dependent variable

known_xs: array of values of independent variables, defaults to a single vector {1,…,n}

affine: if true, the model contains a constant term, defaults to true

stats: if true, some additional statistics are provided, defaults to false

#### Description

This function returns an array with the first row giving the regression coefficients for the independent variables x_m, x_(m-1),…,x_2, x_1 followed by the y-intercept if affine is true.

If stats is true, the second row contains the corresponding standard errors of the regression coefficients.In this case, the third row contains the R^2 value and the standard error for the predicted value. The fourth row contains the observed F value and its degrees of freedom. Finally, the fifth row contains the regression sum of squares and the residual sum of squares.

If affine is false, R^2 is the uncentered version of the coefficient of determination; that is the proportion of the sum of squares explained by the model.

#### Note

If the length of known_ys does not match the corresponding length of known_xs, this function returns a #NUM! error.

#### See also

`LOGEST`, `TREND`.

`LKSTEST`
`LKSTEST` Lilliefors (Kolmogorov-Smirnov) Test of Normality

    LKSTEST(x)

#### Arguments

x: array of sample values

#### Description

This function returns an array with the first row giving the p-value of the Lilliefors (Kolmogorov-Smirnov) Test, the second row the test statistic of the test, and the third the number of observations in the sample.

#### Note

If there are less than 5 sample values, `LKSTEST` returns #VALUE!

#### See also

`CHITEST`, `ADTEST`, `SFTEST`, `CVMTEST`.

`LOGEST`
`LOGEST` exponential least square fit

    LOGEST(known_ys,known_xs,affine,stat)

#### Arguments

known_ys: known y-values

known_xs: known x-values; default to an array {1, 2, 3, …}

affine: if true, the model contains a constant term, defaults to true

stat: if true, extra statistical information will be returned; defaults to FALSE

#### Description

`LOGEST` function applies the “least squares” method to fit an exponential curve of the form y = b * m{1}^x{1} * m{2}^x{2}... to your data.

`LOGEST` returns an array { m{n},m{n-1}, ...,m{1},b }.

#### Note

Extra statistical information is written below the regression line coefficients in the result array. Extra statistical information consists of four rows of data. In the first row the standard error values for the coefficients m1, (m2, ...), b are represented. The second row contains the square of R and the standard error for the y estimate. The third row contains the F-observed value and the degrees of freedom. The last row contains the regression sum of squares and the residual sum of squares. If known_ys and known_xs have unequal number of data points, this function returns a #NUM! error.

#### See also

`GROWTH`, `TREND`.

`LOGFIT`
`LOGFIT` logarithmic least square fit (using a trial and error method)

    LOGFIT(known_ys,known_xs)

#### Arguments

known_ys: known y-values

known_xs: known x-values

#### Description

`LOGFIT` function applies the “least squares” method to fit the logarithmic equation y = a + b * ln(sign * (x - c)) , sign = +1 or -1 to your data. The graph of the equation is a logarithmic curve moved horizontally by c and possibly mirrored across the y-axis (if sign = -1).

`LOGFIT` returns an array having five columns and one row. `Sign' is given in the first column, `a', `b', and `c' are given in columns 2 to 4. Column 5 holds the sum of squared residuals.

#### Note

An error is returned when there are less than 3 different x's or y's, or when the shape of the point cloud is too different from a ``logarithmic'' one. You can use the above formula = a + b * ln(sign * (x - c)) or rearrange it to = (exp((y - a) / b)) / sign + c to compute unknown y's or x's, respectively. This is non-linear fitting by trial-and-error. The accuracy of `c' is: width of x-range -> rounded to the next smaller (10^integer), times 0.000001. There might be cases in which the returned fit is not the best possible.

#### See also

`LOGREG`, `LINEST`, `LOGEST`.

`LOGINV`
`LOGINV` inverse of the cumulative distribution function of the lognormal distribution

    LOGINV(p,mean,stddev)

#### Arguments

p: probability

mean: mean

stddev: standard deviation

#### Note

If p < 0 or p > 1 or stddev <= 0 this function returns #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`EXP`, `LN`, `LOG`, `LOG10`, `LOGNORMDIST`.

`LOGISTIC`
`LOGISTIC` probability density function of the logistic distribution

    LOGISTIC(x,a)

#### Arguments

x: number

a: scale parameter

#### See also

`RANDLOGISTIC`.

`LOGNORMDIST`
`LOGNORMDIST` cumulative distribution function of the lognormal distribution

    LOGNORMDIST(x,mean,stddev)

#### Arguments

x: number

mean: mean

stddev: standard deviation

#### Note

If stddev = 0 `LOGNORMDIST` returns a #DIV/0! error. If x <= 0, mean < 0 or stddev <= 0 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`NORMDIST`.

`LOGREG`
`LOGREG` the logarithmic regression

    LOGREG(known_ys,known_xs,affine,stat)

#### Arguments

known_ys: known y-values

known_xs: known x-values; defaults to the array {1, 2, 3, …}

affine: if true, the model contains a constant term, defaults to true

stat: if true, extra statistical information will be returned; defaults to FALSE

#### Description

`LOGREG` function transforms your x's to z=ln(x) and applies the “least squares” method to fit the linear equation y = m * z + b to your y's and z's --- equivalent to fitting the equation y = m * ln(x) + b to y's and x's. `LOGREG` returns an array having two columns and one row. m is given in the first column and b in the second.

Any extra statistical information is written below m and b in the result array. This extra statistical information consists of four rows of data: In the first row the standard error values for the coefficients m, b are given. The second row contains the square of R and the standard error for the y estimate. The third row contains the F-observed value and the degrees of freedom. The last row contains the regression sum of squares and the residual sum of squares.The default of stat is FALSE.

#### Note

If known_ys and known_xs have unequal number of data points, this function returns a #NUM! error.

#### See also

`LOGFIT`, `LINEST`, `LOGEST`.

`MAX`
`MAX` largest value, with negative numbers considered smaller than positive numbers

    MAX(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`MIN`, `ABS`.

`MAXA`
`MAXA` largest value, with negative numbers considered smaller than positive numbers

    MAXA(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`MAX`, `MINA`.

`MEDIAN`
`MEDIAN` median of a data set

    MEDIAN(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Strings and empty cells are simply ignored.

#### Note

If even numbers are given `MEDIAN` returns the average of the two numbers in the center.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `COUNT`, `COUNTA`, `DAVERAGE`, `MODE`, `SSMEDIAN`, `SUM`.

`MIN`
`MIN` smallest value, with negative numbers considered smaller than positive numbers

    MIN(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`MAX`, `ABS`.

`MINA`
`MINA` smallest value, with negative numbers considered smaller than positive numbers

    MINA(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`MIN`, `MAXA`.

`MODE`
`MODE` first most common number in the dataset

    MODE(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Strings and empty cells are simply ignored.

If the data set does not contain any duplicates this function returns a #N/A error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `MEDIAN`.

`NEGBINOMDIST`
`NEGBINOMDIST` probability mass function of the negative binomial distribution

    NEGBINOMDIST(f,t,p)

#### Arguments

f: number of failures

t: threshold number of successes

p: probability of a success

#### Note

If f or t is a non-integer it is truncated. If (f + t -1) <= 0 this function returns a #NUM! error. If p < 0 or p > 1 this functions returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BINOMDIST`, `COMBIN`, `FACT`, `HYPGEOMDIST`, `PERMUT`.

`NORMDIST`
`NORMDIST` probability density or cumulative distribution function of a normal distribution

    NORMDIST(x,mean,stddev,cumulative)

#### Arguments

x: number

mean: mean of the distribution

stddev: standard deviation of the distribution

cumulative: whether to evaluate the density function or the cumulative distribution function

#### Note

If stddev is 0 this function returns a #DIV/0! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`POISSON`.

`NORMINV`
`NORMINV` inverse of the cumulative distribution function of a normal distribution

    NORMINV(p,mean,stddev)

#### Arguments

p: probability

mean: mean of the distribution

stddev: standard deviation of the distribution

#### Note

If p < 0 or p > 1 or stddev <= 0 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`NORMDIST`, `NORMSDIST`, `NORMSINV`, `STANDARDIZE`, `ZTEST`.

`NORMSDIST`
`NORMSDIST` cumulative density function of the standard normal distribution

    NORMSDIST(x)

#### Arguments

x: number

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`NORMSDIST` is the OpenFormula function LEGACY.`NORMSDIST`.

#### See also

`NORMDIST`.

`NORMSINV`
`NORMSINV` inverse of the cumulative density function of the standard normal distribution

    NORMSINV(p)

#### Arguments

p: given probability

#### Note

If p < 0 or p > 1 this function returns #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

`NORMSINV` is the OpenFormula function LEGACY.`NORMSINV`.

#### See also

`NORMDIST`, `NORMINV`, `NORMSDIST`, `STANDARDIZE`, `ZTEST`.

`PARETO`
`PARETO` probability density function of the pareto distribution

    PARETO(x,a,b)

#### Arguments

x: number

a: exponent

b: scale parameter

#### See also

`RANDPARETO`.

`PEARSON`
`PEARSON` Pearson correlation coefficient of the paired set of data

    PEARSON(array1,array2)

#### Arguments

array1: first component values

array2: second component values

#### Description

Strings and empty cells are simply ignored.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`INTERCEPT`, `LINEST`, `RSQ`, `SLOPE`, `STEYX`.

`PERCENTILE`
`PERCENTILE` determines the 100*k-th percentile of the given data points

    PERCENTILE(array,k)

#### Arguments

array: data points

k: which percentile to calculate

#### Note

If array is empty, this function returns a #NUM! error. If k < 0 or k > 1, this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`QUARTILE`.

`PERCENTRANK`
`PERCENTRANK` rank of a data point in a data set

    PERCENTRANK(array,x,significance)

#### Arguments

array: range of numeric values

x: data point to be ranked

significance: number of significant digits, defaults to 3

#### Note

If array contains no data points, this function returns a #NUM! error. If significance is less than one, this function returns a #NUM! error. If x exceeds the largest value or is less than the smallest value in array, this function returns a #NUM! error. If x does not match any of the values in array or x matches more than once, this function interpolates the returned value.

#### See also

`LARGE`, `MAX`, `MEDIAN`, `MIN`, `PERCENTILE`, `QUARTILE`, `SMALL`.

`PERMUT`
`PERMUT` number of k-permutations of a n-set

    PERMUT(n,k)

#### Arguments

n: size of the base set

k: number of elements in each permutation

#### Note

If n = 0 this function returns a #NUM! error. If n < k this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COMBIN`.

`PERMUTATIONA`
`PERMUTATIONA` the number of permutations of y objects chosen from x objects with repetition allowed

    PERMUTATIONA(x,y)

#### Arguments

x: total number of objects

y: number of selected objects

#### Note

If both x and y equal 0, `PERMUTATIONA` returns 1. If x < 0 or y < 0, `PERMUTATIONA` returns #NUM! If x or y are not integers, they are truncated

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`POWER`.

`POISSON`
`POISSON` probability mass or cumulative distribution function of the Poisson distribution

    POISSON(x,mean,cumulative)

#### Arguments

x: number of events

mean: mean of the distribution

cumulative: whether to evaluate the mass function or the cumulative distribution function

#### Note

If x is a non-integer it is truncated. If x < 0 this function returns a #NUM! error. If mean <= 0 `POISSON` returns the #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`NORMDIST`, `WEIBULL`.

`PROB`
`PROB` probability of an interval for a discrete (and finite) probability distribution

    PROB(x_range,prob_range,lower_limit,upper_limit)

#### Arguments

x_range: possible values

prob_range: probabilities of the corresponding values

lower_limit: lower interval limit

upper_limit: upper interval limit, defaults to lower_limit

#### Note

If the sum of the probabilities in prob_range is not equal to 1 this function returns a #NUM! error. If any value in prob_range is <=0 or > 1, this function returns a #NUM! error. If x_range and prob_range contain a different number of data entries, this function returns a #N/A error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`BINOMDIST`, `CRITBINOM`.

`QUARTILE`
`QUARTILE` the k-th quartile of the data points

    QUARTILE(array,quart)

#### Arguments

array: data points

quart: a number from 0 to 4, indicating which quartile to calculate

#### Note

If array is empty, this function returns a #NUM! error. If quart < 0 or quart > 4, this function returns a #NUM! error. If quart = 0, the smallest value of array to be returned. If quart is not an integer, it is truncated.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`LARGE`, `MAX`, `MEDIAN`, `MIN`, `PERCENTILE`, `SMALL`.

`R.DBETA`
`R.DBETA` probability density function of the beta distribution

    R.DBETA(x,a,b,give_log)

#### Arguments

x: observation

a: the first shape parameter of the distribution

b: the second scale parameter of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the beta distribution.

#### See also

`R.PBETA`, `R.QBETA`.

`R.DBINOM`
`R.DBINOM` probability density function of the binomial distribution

    R.DBINOM(x,n,psuc,give_log)

#### Arguments

x: observation

n: the number of trials

psuc: the probability of success in each trial

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the binomial distribution.

#### See also

`R.PBINOM`, `R.QBINOM`.

`R.DCAUCHY`
`R.DCAUCHY` probability density function of the Cauchy distribution

    R.DCAUCHY(x,location,scale,give_log)

#### Arguments

x: observation

location: the center of the distribution

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the Cauchy distribution.

#### See also

`R.PCAUCHY`, `R.QCAUCHY`.

`R.DCHISQ`
`R.DCHISQ` probability density function of the chi-square distribution

    R.DCHISQ(x,df,give_log)

#### Arguments

x: observation

df: the number of degrees of freedom of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the chi-square distribution.

#### OpenDocument Format (ODF) Compatibility

A two argument invocation `R.DCHISQ`(x,df) is exported to OpenFormula as CHISQDIST(x,df,FALSE()).

#### See also

`R.PCHISQ`, `R.QCHISQ`.

`R.DEXP`
`R.DEXP` probability density function of the exponential distribution

    R.DEXP(x,scale,give_log)

#### Arguments

x: observation

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the exponential distribution.

#### See also

`R.PEXP`, `R.QEXP`.

`R.DF`
`R.DF` probability density function of the F distribution

    R.DF(x,n1,n2,give_log)

#### Arguments

x: observation

n1: the first number of degrees of freedom of the distribution

n2: the second number of degrees of freedom of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the F distribution.

#### See also

`R.PF`, `R.QF`.

`R.DGAMMA`
`R.DGAMMA` probability density function of the gamma distribution

    R.DGAMMA(x,shape,scale,give_log)

#### Arguments

x: observation

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the gamma distribution.

#### See also

`R.PGAMMA`, `R.QGAMMA`.

`R.DGEOM`
`R.DGEOM` probability density function of the geometric distribution

    R.DGEOM(x,psuc,give_log)

#### Arguments

x: observation

psuc: the probability of success in each trial

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the geometric distribution.

#### See also

`R.PGEOM`, `R.QGEOM`.

`R.DHYPER`
`R.DHYPER` probability density function of the hypergeometric distribution

    R.DHYPER(x,r,b,n,give_log)

#### Arguments

x: observation

r: the number of red balls

b: the number of black balls

n: the number of balls drawn

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the hypergeometric distribution.

#### See also

`R.PHYPER`, `R.QHYPER`.

`R.DLNORM`
`R.DLNORM` probability density function of the log-normal distribution

    R.DLNORM(x,logmean,logsd,give_log)

#### Arguments

x: observation

logmean: mean of the underlying normal distribution

logsd: standard deviation of the underlying normal distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the log-normal distribution.

#### See also

`R.PLNORM`, `R.QLNORM`.

`R.DNBINOM`
`R.DNBINOM` probability density function of the negative binomial distribution

    R.DNBINOM(x,n,psuc,give_log)

#### Arguments

x: observation

n: the number of trials

psuc: the probability of success in each trial

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the negative binomial distribution.

#### See also

`R.PNBINOM`, `R.QNBINOM`.

`R.DNORM`
`R.DNORM` probability density function of the normal distribution

    R.DNORM(x,mu,sigma,give_log)

#### Arguments

x: observation

mu: mean of the distribution

sigma: standard deviation of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the normal distribution.

#### See also

`R.PNORM`, `R.QNORM`.

`R.DPOIS`
`R.DPOIS` probability density function of the Poisson distribution

    R.DPOIS(x,lambda,give_log)

#### Arguments

x: observation

lambda: the mean of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the Poisson distribution.

#### See also

`R.PPOIS`, `R.QPOIS`.

`R.DSNORM`
`R.DSNORM` probability density function of the skew-normal distribution

    R.DSNORM(x,shape,location,scale,give_log)

#### Arguments

x: observation

shape: the shape parameter of the distribution

location: the location parameter of the distribution

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the skew-normal distribution.

#### See also

`R.PSNORM`.

`R.DST`
`R.DST` probability density function of the skew-t distribution

    R.DST(x,n,shape,give_log)

#### Arguments

x: observation

n: the number of degrees of freedom of the distribution

shape: the shape parameter of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the skew-t distribution.

`R.DT`
`R.DT` probability density function of the Student t distribution

    R.DT(x,n,give_log)

#### Arguments

x: observation

n: the number of degrees of freedom of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the Student t distribution.

#### See also

`R.PT`, `R.QT`.

`R.DWEIBULL`
`R.DWEIBULL` probability density function of the Weibull distribution

    R.DWEIBULL(x,shape,scale,give_log)

#### Arguments

x: observation

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

#### Description

This function returns the probability density function of the Weibull distribution.

#### See also

`R.PWEIBULL`, `R.QWEIBULL`.

`R.PBETA`
`R.PBETA` cumulative distribution function of the beta distribution

    R.PBETA(x,a,b,lower_tail,log_p)

#### Arguments

x: observation

a: the first shape parameter of the distribution

b: the second scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the beta distribution.

#### See also

`R.DBETA`, `R.QBETA`.

`R.PBINOM`
`R.PBINOM` cumulative distribution function of the binomial distribution

    R.PBINOM(x,n,psuc,lower_tail,log_p)

#### Arguments

x: observation

n: the number of trials

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the binomial distribution.

#### See also

`R.DBINOM`, `R.QBINOM`.

`R.PCAUCHY`
`R.PCAUCHY` cumulative distribution function of the Cauchy distribution

    R.PCAUCHY(x,location,scale,lower_tail,log_p)

#### Arguments

x: observation

location: the center of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the Cauchy distribution.

#### See also

`R.DCAUCHY`, `R.QCAUCHY`.

`R.PCHISQ`
`R.PCHISQ` cumulative distribution function of the chi-square distribution

    R.PCHISQ(x,df,lower_tail,log_p)

#### Arguments

x: observation

df: the number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the chi-square distribution.

#### OpenDocument Format (ODF) Compatibility

A two argument invocation `R.PCHISQ`(x,df) is exported to OpenFormula as CHISQDIST(x,df).

#### See also

`R.DCHISQ`, `R.QCHISQ`.

`R.PEXP`
`R.PEXP` cumulative distribution function of the exponential distribution

    R.PEXP(x,scale,lower_tail,log_p)

#### Arguments

x: observation

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the exponential distribution.

#### See also

`R.DEXP`, `R.QEXP`.

`R.PF`
`R.PF` cumulative distribution function of the F distribution

    R.PF(x,n1,n2,lower_tail,log_p)

#### Arguments

x: observation

n1: the first number of degrees of freedom of the distribution

n2: the second number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the F distribution.

#### See also

`R.DF`, `R.QF`.

`R.PGAMMA`
`R.PGAMMA` cumulative distribution function of the gamma distribution

    R.PGAMMA(x,shape,scale,lower_tail,log_p)

#### Arguments

x: observation

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the gamma distribution.

#### See also

`R.DGAMMA`, `R.QGAMMA`.

`R.PGEOM`
`R.PGEOM` cumulative distribution function of the geometric distribution

    R.PGEOM(x,psuc,lower_tail,log_p)

#### Arguments

x: observation

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the geometric distribution.

#### See also

`R.DGEOM`, `R.QGEOM`.

`R.PHYPER`
`R.PHYPER` cumulative distribution function of the hypergeometric distribution

    R.PHYPER(x,r,b,n,lower_tail,log_p)

#### Arguments

x: observation

r: the number of red balls

b: the number of black balls

n: the number of balls drawn

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the hypergeometric distribution.

#### See also

`R.DHYPER`, `R.QHYPER`.

`R.PLNORM`
`R.PLNORM` cumulative distribution function of the log-normal distribution

    R.PLNORM(x,logmean,logsd,lower_tail,log_p)

#### Arguments

x: observation

logmean: mean of the underlying normal distribution

logsd: standard deviation of the underlying normal distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the log-normal distribution.

#### See also

`R.DLNORM`, `R.QLNORM`.

`R.PNBINOM`
`R.PNBINOM` cumulative distribution function of the negative binomial distribution

    R.PNBINOM(x,n,psuc,lower_tail,log_p)

#### Arguments

x: observation

n: the number of trials

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the negative binomial distribution.

#### See also

`R.DNBINOM`, `R.QNBINOM`.

`R.PNORM`
`R.PNORM` cumulative distribution function of the normal distribution

    R.PNORM(x,mu,sigma,lower_tail,log_p)

#### Arguments

x: observation

mu: mean of the distribution

sigma: standard deviation of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the normal distribution.

#### See also

`R.DNORM`, `R.QNORM`.

`R.PPOIS`
`R.PPOIS` cumulative distribution function of the Poisson distribution

    R.PPOIS(x,lambda,lower_tail,log_p)

#### Arguments

x: observation

lambda: the mean of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the Poisson distribution.

#### See also

`R.DPOIS`, `R.QPOIS`.

`R.PSNORM`
`R.PSNORM` cumulative distribution function of the skew-normal distribution

    R.PSNORM(x,shape,location,scale,lower_tail,log_p)

#### Arguments

x: observation

shape: the shape parameter of the distribution

location: the location parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the skew-normal distribution.

#### See also

`R.DSNORM`.

`R.PT`
`R.PT` cumulative distribution function of the Student t distribution

    R.PT(x,n,lower_tail,log_p)

#### Arguments

x: observation

n: the number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the Student t distribution.

#### See also

`R.DT`, `R.QT`.

`R.PWEIBULL`
`R.PWEIBULL` cumulative distribution function of the Weibull distribution

    R.PWEIBULL(x,shape,scale,lower_tail,log_p)

#### Arguments

x: observation

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the cumulative distribution function of the Weibull distribution.

#### See also

`R.DWEIBULL`, `R.QWEIBULL`.

`R.QBETA`
`R.QBETA` probability quantile function of the beta distribution

    R.QBETA(p,a,b,lower_tail,log_p)

#### Arguments

p: probability

a: the first shape parameter of the distribution

b: the second scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the beta distribution.

#### See also

`R.DBETA`, `R.PBETA`.

`R.QBINOM`
`R.QBINOM` probability quantile function of the binomial distribution

    R.QBINOM(x,n,psuc,lower_tail,log_p)

#### Arguments

x: observation

n: the number of trials

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the binomial distribution.

#### See also

`R.DBINOM`, `R.PBINOM`.

`R.QCAUCHY`
`R.QCAUCHY` probability quantile function of the Cauchy distribution

    R.QCAUCHY(p,location,scale,lower_tail,log_p)

#### Arguments

p: probability

location: the center of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Cauchy distribution.

#### See also

`R.DCAUCHY`, `R.PCAUCHY`.

`R.QCHISQ`
`R.QCHISQ` probability quantile function of the chi-square distribution

    R.QCHISQ(p,df,lower_tail,log_p)

#### Arguments

p: probability

df: the number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the chi-square distribution.

#### OpenDocument Format (ODF) Compatibility

A two argument invocation `R.QCHISQ`(p,df) is exported to OpenFormula as CHISQINV(p,df).

#### See also

`R.DCHISQ`, `R.PCHISQ`.

`R.QEXP`
`R.QEXP` probability quantile function of the exponential distribution

    R.QEXP(p,scale,lower_tail,log_p)

#### Arguments

p: probability

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the exponential distribution.

#### See also

`R.DEXP`, `R.PEXP`.

`R.QF`
`R.QF` probability quantile function of the F distribution

    R.QF(x,n1,n2,lower_tail,log_p)

#### Arguments

x: observation

n1: the first number of degrees of freedom of the distribution

n2: the second number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the F distribution.

#### See also

`R.DF`, `R.PF`.

`R.QGAMMA`
`R.QGAMMA` probability quantile function of the gamma distribution

    R.QGAMMA(p,shape,scale,lower_tail,log_p)

#### Arguments

p: probability

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the gamma distribution.

#### See also

`R.DGAMMA`, `R.PGAMMA`.

`R.QGEOM`
`R.QGEOM` probability quantile function of the geometric distribution

    R.QGEOM(p,psuc,lower_tail,log_p)

#### Arguments

p: probability

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the geometric distribution.

#### See also

`R.DGEOM`, `R.PGEOM`.

`R.QHYPER`
`R.QHYPER` probability quantile function of the hypergeometric distribution

    R.QHYPER(p,r,b,n,lower_tail,log_p)

#### Arguments

p: probability

r: the number of red balls

b: the number of black balls

n: the number of balls drawn

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the hypergeometric distribution.

#### See also

`R.DHYPER`, `R.PHYPER`.

`R.QLNORM`
`R.QLNORM` probability quantile function of the log-normal distribution

    R.QLNORM(x,logmean,logsd,lower_tail,log_p)

#### Arguments

x: observation

logmean: mean of the underlying normal distribution

logsd: standard deviation of the underlying normal distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the log-normal distribution.

#### See also

`R.DLNORM`, `R.PLNORM`.

`R.QNBINOM`
`R.QNBINOM` probability quantile function of the negative binomial distribution

    R.QNBINOM(p,n,psuc,lower_tail,log_p)

#### Arguments

p: probability

n: the number of trials

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the negative binomial distribution.

#### See also

`R.DNBINOM`, `R.PNBINOM`.

`R.QNORM`
`R.QNORM` probability quantile function of the normal distribution

    R.QNORM(p,mu,sigma,lower_tail,log_p)

#### Arguments

p: probability

mu: mean of the distribution

sigma: standard deviation of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the normal distribution.

#### See also

`R.DNORM`, `R.PNORM`.

`R.QPOIS`
`R.QPOIS` probability quantile function of the Poisson distribution

    R.QPOIS(p,lambda,lower_tail,log_p)

#### Arguments

p: probability

lambda: the mean of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Poisson distribution.

#### See also

`R.DPOIS`, `R.PPOIS`.

`R.QT`
`R.QT` probability quantile function of the Student t distribution

    R.QT(p,n,lower_tail,log_p)

#### Arguments

p: probability

n: the number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Student t distribution.

#### See also

`R.DT`, `R.PT`.

`R.QWEIBULL`
`R.QWEIBULL` probability quantile function of the Weibull distribution

    R.QWEIBULL(p,shape,scale,lower_tail,log_p)

#### Arguments

p: probability

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, log of the probability is used

#### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Weibull distribution.

#### See also

`R.DWEIBULL`, `R.PWEIBULL`.

`RANK`
`RANK` rank of a number in a list of numbers

    RANK(x,ref,order)

#### Arguments

x: number whose rank you want to find

ref: list of numbers

order: 0 (descending order) or non-zero (ascending order); defaults to 0

#### Note

In case of a tie, `RANK` returns the largest possible rank.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`PERCENTRANK`, `RANK.AVG`.

`RANK.AVG`
`RANK.AVG` rank of a number in a list of numbers

    RANK.AVG(x,ref,order)

#### Arguments

x: number whose rank you want to find

ref: list of numbers

order: 0 (descending order) or non-zero (ascending order); defaults to 0

#### Note

In case of a tie, RANK returns the average rank.

#### Microsoft Excel Compatibility

This function is Excel 2010 compatible.

#### See also

`PERCENTRANK`, `RANK`.

`RAYLEIGH`
`RAYLEIGH` probability density function of the Rayleigh distribution

    RAYLEIGH(x,sigma)

#### Arguments

x: number

sigma: scale parameter

#### See also

`RANDRAYLEIGH`.

`RAYLEIGHTAIL`
`RAYLEIGHTAIL` probability density function of the Rayleigh tail distribution

    RAYLEIGHTAIL(x,a,sigma)

#### Arguments

x: number

a: lower limit

sigma: scale parameter

#### See also

`RANDRAYLEIGHTAIL`.

`RSQ`
`RSQ` square of the Pearson correlation coefficient of the paired set of data

    RSQ(array1,array2)

#### Arguments

array1: first component values

array2: second component values

#### Description

Strings and empty cells are simply ignored.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CORREL`, `COVAR`, `INTERCEPT`, `LINEST`, `LOGEST`, `PEARSON`, `SLOPE`, `STEYX`, `TREND`.

`SFTEST`
`SFTEST` Shapiro-Francia Test of Normality

    SFTEST(x)

#### Arguments

x: array of sample values

#### Description

This function returns an array with the first row giving the p-value of the Shapiro-Francia Test, the second row the test statistic of the test, and the third the number of observations in the sample.

#### Note

If there are less than 5 or more than 5000 sample values, `SFTEST` returns #VALUE!

#### See also

`CHITEST`, `ADTEST`, `LKSTEST`, `CVMTEST`.

`SKEW`
`SKEW` unbiased estimate for skewness of a distribution

    SKEW(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Strings and empty cells are simply ignored.

#### Note

This is only meaningful if the underlying distribution really has a third moment. The skewness of a symmetric (e.g., normal) distribution is zero. If less than three numbers are given, this function returns a #DIV/0! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `VAR`, `SKEWP`, `KURT`.

`SKEWP`
`SKEWP` population skewness of a data set

    SKEWP(number1,number2)

#### Arguments

number1: first value

number2: second value

#### Description

Strings and empty cells are simply ignored.

#### Note

If less than two numbers are given, `SKEWP` returns a #DIV/0! error.

#### See also

`AVERAGE`, `VARP`, `SKEW`, `KURTP`.

`SLOPE`
`SLOPE` the slope of a linear regression line

    SLOPE(known_ys,known_xs)

#### Arguments

known_ys: known y-values

known_xs: known x-values

#### Note

If known_xs or known_ys contains no data entries or different number of data entries, this function returns a #N/A error. If the variance of the known_xs is zero, this function returns #DIV/0 error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`STDEV`, `STDEVPA`.

`SMALL`
`SMALL` k-th smallest value in a data set

    SMALL(data,k)

#### Arguments

data: data set

k: which value to find

#### Note

If data set is empty this function returns a #NUM! error. If k <= 0 or k is greater than the number of data items given this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`PERCENTILE`, `PERCENTRANK`, `QUARTILE`, `LARGE`.

`SSMEDIAN`
`SSMEDIAN` median for grouped data as commonly determined in the social sciences

    SSMEDIAN(array,interval)

#### Arguments

array: data set

interval: length of each grouping interval, defaults to 1

#### Description

The data points given in array are assumed to be the result of grouping data into intervals of length interval

#### Note

If array is empty, this function returns a #NUM! error. If interval <= 0, this function returns a #NUM! error.`SSMEDIAN` does not check whether the data points are at least interval apart.

#### See also

`MEDIAN`.

`STANDARDIZE`
`STANDARDIZE` z-score of a value

    STANDARDIZE(x,mean,stddev)

#### Arguments

x: value

mean: mean of the original distribution

stddev: standard deviation of the original distribution

#### Note

If stddev is 0 this function returns a #DIV/0! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`.

`STDEV`
`STDEV` sample standard deviation of the given sample

    STDEV(area1,area2)

#### Arguments

area1: first cell area

area2: second cell area

#### Description

`STDEV` is also known as the N-1-standard deviation.

To obtain the population standard deviation of a whole population use STDEVP.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `DSTDEV`, `DSTDEVP`, `STDEVA`, `STDEVPA`, `VAR`.

`STDEVA`
`STDEVA` sample standard deviation of the given sample

    STDEVA(area1,area2)

#### Arguments

area1: first cell area

area2: second cell area

#### Description

`STDEVA` is also known as the N-1-standard deviation.

To obtain the population standard deviation of a whole population use STDEVPA.

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`STDEV`, `STDEVPA`.

`STDEVP`
`STDEVP` population standard deviation of the given population

    STDEVP(area1,area2)

#### Arguments

area1: first cell area

area2: second cell area

#### Description

This is also known as the N-standard deviation

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`STDEV`, `STDEVA`, `STDEVPA`.

`STDEVPA`
`STDEVPA` population standard deviation of an entire population

    STDEVPA(area1,area2)

#### Arguments

area1: first cell area

area2: second cell area

#### Description

This is also known as the N-standard deviation

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`STDEVA`, `STDEVP`.

`STEYX`
`STEYX` standard error of the predicted y-value in the regression

    STEYX(known_ys,known_xs)

#### Arguments

known_ys: known y-values

known_xs: known x-values

#### Note

If known_ys and known_xs are empty or have a different number of arguments then this function returns a #N/A error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`PEARSON`, `RSQ`, `SLOPE`.

`SUBTOTAL`
`SUBTOTAL` the subtotal of the given list of arguments

    SUBTOTAL(function_nbr,ref1,ref2)

#### Arguments

function_nbr: determines which function to use according to the following table:

1 AVERAGE

2 COUNT

3 COUNTA

4 MAX

5 MIN

6 PRODUCT

7 STDEV

8 STDEVP

9 SUM

10 VAR

11 VARP

ref1: first value

ref2: second value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`COUNT`, `SUM`.

`TDIST`
`TDIST` survival function of the Student t-distribution

    TDIST(x,dof,tails)

#### Arguments

x: number

dof: number of degrees of freedom

tails: 1 or 2

#### Description

The survival function is 1 minus the cumulative distribution function.

This function is Excel compatible for non-negative x.

#### Note

If dof < 1 this function returns a #NUM! error. If tails is neither 1 or 2 this function returns a #NUM! error. The parameterization of this function is different from what is used for, e.g., NORMSDIST. This is a common source of mistakes, but necessary for compatibility.

#### See also

`TINV`, `TTEST`.

`TINV`
`TINV` inverse of the survival function of the Student t-distribution

    TINV(p,dof)

#### Arguments

p: probability

dof: number of degrees of freedom

#### Description

The survival function is 1 minus the cumulative distribution function.

#### Note

If p < 0 or p > 1 or dof < 1 this function returns a #NUM! error. The parameterization of this function is different from what is used for, e.g., NORMSINV. This is a common source of mistakes, but necessary for compatibility.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TDIST`, `TTEST`.

`TREND`
`TREND` estimates future values of a given data set using a least squares approximation

    TREND(known_ys,known_xs,new_xs,affine)

#### Arguments

known_ys: known y-values

known_xs: known x-values; defaults to the array {1, 2, 3, …}

new_xs: x-values for which to estimate the y-values; defaults to known_xs

affine: if true, the model contains a constant term, defaults to true

#### Note

If known_ys and known_xs have unequal number of data points, this function returns a #NUM! error.

#### See also

`LINEST`.

`TRIMMEAN`
`TRIMMEAN` mean of the interior of a data set

    TRIMMEAN(ref,fraction)

#### Arguments

ref: list of numbers whose mean you want to calculate

fraction: fraction of the data set excluded from the mean

#### Description

If fraction=0.2 and the data set contains 40 numbers, 8 numbers are trimmed from the data set (40 x 0.2): the 4 largest and the 4 smallest. To avoid a bias, the number of points to be excluded is always rounded down to the nearest even number.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`AVERAGE`, `GEOMEAN`, `HARMEAN`, `MEDIAN`, `MODE`.

`TTEST`
`TTEST` p-value for a hypothesis test comparing the means of two populations using the Student t-distribution

    TTEST(array1,array2,tails,type)

#### Arguments

array1: sample from the first population

array2: sample from the second population

tails: number of tails to consider

type: Type of test to perform. 1 indicates a test for paired variables, 2 a test of unpaired variables with equal variances, and 3 a test of unpaired variables with unequal variances

#### Note

If the data sets contain a different number of data points and the test is paired (type one), `TTEST` returns the #N/A error. tails and type are truncated to integers. If tails is not one or two, this function returns a #NUM! error. If type is any other than one, two, or three, this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FDIST`, `FINV`.

`VAR`
`VAR` sample variance of the given sample

    VAR(area1,area2)

#### Arguments

area1: first cell area

area2: second cell area

#### Description

`VAR` is also known as the N-1-variance.

#### Note

Since the N-1-variance includes Bessel's correction, whereas the N-variance calculated by VARPA or VARP does not, under reasonable conditions the N-1-variance is an unbiased estimator of the variance of the population from which the sample is drawn.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`VARP`, `STDEV`, `VARA`.

`VARA`
`VARA` sample variance of the given sample

    VARA(area1,area2)

#### Arguments

area1: first cell area

area2: second cell area

#### Description

`VARA` is also known as the N-1-variance.

To get the true variance of a complete population use VARPA.

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

#### Note

Since the N-1-variance includes Bessel's correction, whereas the N-variance calculated by VARPA or VARP does not, under reasonable conditions the N-1-variance is an unbiased estimator of the variance of the population from which the sample is drawn.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`VAR`, `VARPA`.

`VARP`
`VARP` variance of an entire population

    VARP(area1,area2)

#### Arguments

area1: first cell area

area2: second cell area

#### Description

`VARP` is also known as the N-variance.

#### See also

`AVERAGE`, `DVAR`, `DVARP`, `STDEV`, `VAR`.

`VARPA`
`VARPA` variance of an entire population

    VARPA(area1,area2)

#### Arguments

area1: first cell area

area2: second cell area

#### Description

`VARPA` is also known as the N-variance.

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`VARA`, `VARP`.

`WEIBULL`
`WEIBULL` probability density or cumulative distribution function of the Weibull distribution

    WEIBULL(x,alpha,beta,cumulative)

#### Arguments

x: number

alpha: scale parameter

beta: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

#### Description

If the cumulative boolean is true it will return: 1 - exp (-(x/beta)^alpha),otherwise it will return (alpha/beta^alpha) * x^(alpha-1) * exp(-(x/beta^alpha)).

#### Note

If x < 0 this function returns a #NUM! error. If alpha <= 0 or beta <= 0 this function returns a #NUM! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`POISSON`.

`ZTEST`
`ZTEST` the probability of observing a sample mean as large as or larger than the mean of the given sample

    ZTEST(ref,x,stddev)

#### Arguments

ref: data set (sample)

x: population mean

stddev: population standard deviation, defaults to the sample standard deviation

#### Description

`ZTEST` calulates the probability of observing a sample mean as large as or larger than the mean of the given sample for samples drawn from a normal distribution with mean x and standard deviation stddev.

#### Note

If ref contains less than two data items `ZTEST` returns #DIV/0! error.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`CONFIDENCE`, `NORMDIST`, `NORMINV`, `NORMSDIST`, `NORMSINV`, `STANDARDIZE`.

## String

`ASC`
`ASC` text with full-width katakana and ASCII characters converted to half-width

    ASC(text)

#### Arguments

text: string

#### Description

`ASC` converts full-width katakana and ASCII characters to half-width equivalent characters, copying all others.

The distinction between half-width and full-width characters is described in http://www.unicode.org/reports/tr11/.

#### Note

While in obsolete encodings `ASC` used to translate between 2-byte and 1-byte characters, this is not the case in UTF-8.

#### Microsoft Excel Compatibility

For most strings, this function has the same effect as in Excel.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`JIS`.

`CHAR`
`CHAR` the CP1252 (Windows-1252) character for the code point x

    CHAR(x)

#### Arguments

x: code point

#### Description

`CHAR`(x) returns the CP1252 (Windows-1252) character with code x.

x must be in the range 1 to 255.

CP1252 (Windows-1252) is also known as the "ANSI code page", but it is not an ANSI standard.

CP1252 (Windows-1252) is based on an early draft of ISO-8859-1, and contains all of its printable characters. It also contains all of ISO-8859-15's printable characters (but partially at different positions.)

This function is Excel compatible.

#### Note

In CP1252 (Windows-1252), 129, 141, 143, 144, and 157 do not have matching characters. For x from 1 to 255 except 129, 141, 143, 144, and 157 we have CODE(`CHAR`(x))=x.

#### See also

`CODE`.

`CLEAN`
`CLEAN` text with any non-printable characters removed

    CLEAN(text)

#### Arguments

text: string

#### Description

`CLEAN` removes non-printable characters from its argument leaving only regular characters and white-space.

#### Microsoft Excel Compatibility

This function is Excel compatible.

`CODE`
`CODE` the CP1252 (Windows-1252) code point for the character c

    CODE(c)

#### Arguments

c: character

#### Description

c must be a valid CP1252 (Windows-1252) character.

CP1252 (Windows-1252) is also known as the "ANSI code page", but it is not an ANSI standard.

CP1252 (Windows-1252) is based on an early draft of ISO-8859-1, and contains all of its printable characters (but partially at different positions.)

This function is Excel compatible.

#### Note

In CP1252 (Windows-1252), 129, 141, 143, 144, and 157 do not have matching characters. For x from 1 to 255 except 129, 141, 143, 144, and 157 we have `CODE`(CHAR(x))=x.

#### See also

`CHAR`.

`CONCATENATE`
`CONCATENATE` the concatenation of the strings s1, s2,…

    CONCATENATE(s1,s2)

#### Arguments

s1: first string

s2: second string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`LEFT`, `MID`, `RIGHT`.

`DOLLAR`
`DOLLAR` num formatted as currency

    DOLLAR(num,decimals)

#### Arguments

num: number

decimals: decimals

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FIXED`, `TEXT`, `VALUE`.

`EXACT`
`EXACT` TRUE if string1 is exactly equal to string2

    EXACT(string1,string2)

#### Arguments

string1: first string

string2: second string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`LEN`, `SEARCH`, `DELTA`.

`FIND`
`FIND` first position of string1 in string2 following position start

    FIND(string1,string2,start)

#### Arguments

string1: search string

string2: search field

start: starting position, defaults to 1

#### Note

This search is case-sensitive.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`EXACT`, `LEN`, `MID`, `SEARCH`.

`FINDB`
`FINDB` first byte position of string1 in string2 following byte position start

    FINDB(string1,string2,start)

#### Arguments

string1: search string

string2: search field

start: starting byte position, defaults to 1

#### Note

This search is case-sensitive.

#### Microsoft Excel Compatibility

While this function is syntactically Excel compatible, the differences in the underlying text encoding will usually yield different results.

#### OpenDocument Format (ODF) Compatibility

While this function is OpenFormula compatible, most of its behavior is, at this time, implementation specific.

#### See also

`FIND`, `LEFTB`, `RIGHTB`, `LENB`, `LEFT`, `MID`, `RIGHT`, `LEN`.

`FIXED`
`FIXED` formatted string representation of num

    FIXED(num,decimals,no_commas)

#### Arguments

num: number

decimals: number of decimals

no_commas: TRUE if no thousand separators should be used, defaults to FALSE

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`TEXT`, `VALUE`, `DOLLAR`.

`JIS`
`JIS` text with half-width katakana and ASCII characters converted to full-width

    JIS(text)

#### Arguments

text: original text

#### Description

`JIS` converts half-width katakana and ASCII characters to full-width equivalent characters, copying all others.

The distinction between half-width and full-width characters is described in http://www.unicode.org/reports/tr11/.

#### Note

While in obsolete encodings `JIS` used to translate between 1-byte and 2-byte characters, this is not the case in UTF-8.

#### Microsoft Excel Compatibility

For most strings, this function has the same effect as in Excel.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`ASC`.

`LEFT`
`LEFT` the first num_chars characters of the string s

    LEFT(s,num_chars)

#### Arguments

s: the string

num_chars: the number of characters to return (defaults to 1)

#### Note

If the string s is in a right-to-left script, the returned first characters are from the right of the string.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`MID`, `RIGHT`, `LEN`, `MIDB`, `RIGHTB`, `LENB`.

`LEFTB`
`LEFTB` the first characters of the string s comprising at most num_bytes bytes

    LEFTB(s,num_bytes)

#### Arguments

s: the string

num_bytes: the maximum number of bytes to return (defaults to 1)

#### Note

The semantics of this function is subject to change as various applications implement it. If the string is in a right-to-left script, the returned first characters are from the right of the string.

#### Microsoft Excel Compatibility

While this function is syntactically Excel compatible, the differences in the underlying text encoding will usually yield different results.

#### OpenDocument Format (ODF) Compatibility

While this function is OpenFormula compatible, most of its behavior is, at this time, implementation specific.

#### See also

`MIDB`, `RIGHTB`, `LENB`, `LEFT`, `MID`, `RIGHT`, `LEN`.

`LEN`
`LEN` the number of characters of the string s

    LEN(s)

#### Arguments

s: the string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CHAR`, `CODE`, `LENB`.

`LENB`
`LENB` the number of bytes in the string s

    LENB(s)

#### Arguments

s: the string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CHAR`, `CODE`, `LEN`.

`LOWER`
`LOWER` a lower-case version of the string text

    LOWER(text)

#### Arguments

text: string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`UPPER`.

`MID`
`MID` the substring of the string s starting at position position consisting of length characters

    MID(s,position,length)

#### Arguments

s: the string

position: the starting position

length: the number of characters to return

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`LEFT`, `RIGHT`, `LEN`, `LEFTB`, `MIDB`, `RIGHTB`, `LENB`.

`MIDB`
`MIDB` the characters following the first start_pos bytes comprising at most num_bytes bytes

    MIDB(s,start_pos,num_bytes)

#### Arguments

s: the string

start_pos: the number of the byte with which to start (defaults to 1)

num_bytes: the maximum number of bytes to return (defaults to 1)

#### Note

The semantics of this function is subject to change as various applications implement it.

#### Microsoft Excel Compatibility

While this function is syntactically Excel compatible, the differences in the underlying text encoding will usually yield different results.

#### OpenDocument Format (ODF) Compatibility

While this function is OpenFormula compatible, most of its behavior is, at this time, implementation specific.

#### See also

`LEFTB`, `RIGHTB`, `LENB`, `LEFT`, `MID`, `RIGHT`, `LEN`.

`NUMBERVALUE`
`NUMBERVALUE` numeric value of text

    NUMBERVALUE(text,separator)

#### Arguments

text: string

separator: decimal separator

#### Note

If text does not look like a decimal number, `NUMBERVALUE` returns the value VALUE would return (ignoring the given separator).

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`VALUE`.

`PROPER`
`PROPER` text with initial of each word capitalised

    PROPER(text)

#### Arguments

text: string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`LOWER`, `UPPER`.

`REPLACE`
`REPLACE` string old with num characters starting at start replaced by new

    REPLACE(old,start,num,new)

#### Arguments

old: original text

start: starting position

num: number of characters to be replaced

new: replacement string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`MID`, `SEARCH`, `SUBSTITUTE`, `TRIM`.

`REPLACEB`
`REPLACEB` string old with up to num bytes starting at start replaced by new

    REPLACEB(old,start,num,new)

#### Arguments

old: original text

start: starting byte position

num: number of bytes to be replaced

new: replacement string

#### Description

`REPLACEB` replaces the string of valid unicode characters starting at the byte start and ending at start+num-1 with the string new.

#### Note

The semantics of this function is subject to change as various applications implement it.

#### Microsoft Excel Compatibility

While this function is syntactically Excel compatible, the differences in the underlying text encoding will usually yield different results.

#### OpenDocument Format (ODF) Compatibility

While this function is OpenFormula compatible, most of its behavior is, at this time, implementation specific.

#### See also

`MID`, `SEARCH`, `SUBSTITUTE`, `TRIM`.

`REPT`
`REPT` num repetitions of string text

    REPT(text,num)

#### Arguments

text: string

num: non-negative integer

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CONCATENATE`.

`RIGHT`
`RIGHT` the last num_chars characters of the string s

    RIGHT(s,num_chars)

#### Arguments

s: the string

num_chars: the number of characters to return (defaults to 1)

#### Note

If the string s is in a right-to-left script, the returned last characters are from the left of the string.

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

#### See also

`LEFT`, `MID`, `LEN`, `LEFTB`, `MIDB`, `RIGHTB`, `LENB`.

`RIGHTB`
`RIGHTB` the last characters of the string s comprising at most num_bytes bytes

    RIGHTB(s,num_bytes)

#### Arguments

s: the string

num_bytes: the maximum number of bytes to return (defaults to 1)

#### Note

The semantics of this function is subject to change as various applications implement it. If the string s is in a right-to-left script, the returned last characters are from the left of the string.

#### Microsoft Excel Compatibility

While this function is syntactically Excel compatible, the differences in the underlying text encoding will usually yield different results.

#### OpenDocument Format (ODF) Compatibility

While this function is OpenFormula compatible, most of its behavior is, at this time, implementation specific.

#### See also

`LEFTB`, `MIDB`, `LENB`, `LEFT`, `MID`, `RIGHT`, `LEN`.

`SEARCH`
`SEARCH` the location of the search string within text after position start

    SEARCH(search,text,start)

#### Arguments

search: search string

text: search field

start: starting position, defaults to 1

#### Description

search may contain wildcard characters (*) and question marks (?). A question mark matches any single character, and a wildcard matches any string including the empty string. To search for * or ?, precede the symbol with ~.

#### Note

This search is not case sensitive. If search is not found, `SEARCH` returns #VALUE! If start is less than one or it is greater than the length of text, `SEARCH` returns #VALUE!

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`FIND`, `SEARCHB`.

`SEARCHB`
`SEARCHB` the location of the search string within text after byte position start

    SEARCHB(search,text,start)

#### Arguments

search: search string

text: search field

start: starting byte position, defaults to 1

#### Description

search may contain wildcard characters (*) and question marks (?). A question mark matches any single character, and a wildcard matches any string including the empty string. To search for * or ?, precede the symbol with ~.

#### Note

This search is not case sensitive. If search is not found, `SEARCHB` returns #VALUE! If start is less than one or it is greater than the byte length of text, `SEARCHB` returns #VALUE! The semantics of this function is subject to change as various applications implement it.

#### Microsoft Excel Compatibility

While this function is syntactically Excel compatible, the differences in the underlying text encoding will usually yield different results.

#### OpenDocument Format (ODF) Compatibility

While this function is OpenFormula compatible, most of its behavior is, at this time, implementation specific.

#### See also

`FINDB`, `SEARCH`.

`SUBSTITUTE`
`SUBSTITUTE` text with all occurrences of old replaced by new

    SUBSTITUTE(text,old,new,num)

#### Arguments

text: original text

old: string to be replaced

new: replacement string

num: if num is specified and a number only the numth occurrence of old is replaced

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`REPLACE`, `TRIM`.

`T`
`T` value if and only if value is text, otherwise empty

    T(value)

#### Arguments

value: original value

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CELL`, `N`, `VALUE`.

`TEXT`
`TEXT` value as a string formatted as format

    TEXT(value,format)

#### Arguments

value: value to be formatted

format: desired format

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DOLLAR`, `FIXED`, `VALUE`.

`TRIM`
`TRIM` text with only single spaces between words

    TRIM(text)

#### Arguments

text: string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`CLEAN`, `MID`, `REPLACE`, `SUBSTITUTE`.

`UNICHAR`
`UNICHAR` the Unicode character represented by the Unicode code point x

    UNICHAR(x)

#### Arguments

x: Unicode code point

#### See also

`CHAR`, `UNICODE`, `CODE`.

`UNICODE`
`UNICODE` the Unicode code point for the character c

    UNICODE(c)

#### Arguments

c: character

#### See also

`UNICHAR`, `CODE`, `CHAR`.

`UPPER`
`UPPER` an upper-case version of the string text

    UPPER(text)

#### Arguments

text: string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`LOWER`.

`VALUE`
`VALUE` numeric value of text

    VALUE(text)

#### Arguments

text: string

#### Microsoft Excel Compatibility

This function is Excel compatible.

#### See also

`DOLLAR`, `FIXED`, `TEXT`.

## Time Series Analysis

`FOURIER`
`FOURIER` Fourier or inverse Fourier transform

    FOURIER(Sequence,Inverse,Separate)

#### Arguments

Sequence: the data sequence to be transformed

Inverse: if true, the inverse Fourier transform is calculated, defaults to false

Separate: if true, the real and imaginary parts are given separately, defaults to false

#### Description

This array function returns the Fourier or inverse Fourier transform of the given data sequence.

The output consists of one column of complex numbers if Separate is false and of two columns of real numbers if Separate is true.

If Separate is true the first output column contains the real parts and the second column the imaginary parts.

#### Note

If Sequence is neither an n by 1 nor 1 by n array, this function returns #NUM!

`INTERPOLATION`
`INTERPOLATION` interpolated values corresponding to the given abscissa targets

    INTERPOLATION(abscissae,ordinates,targets,interpolation)

#### Arguments

abscissae: ordered abscissae of the given data points

ordinates: ordinates of the given data points

targets: abscissae of the interpolated data

interpolation: method of interpolation, defaults to 0 ('linear')

#### Description

The output consists always of one column of numbers.

Possible interpolation methods are:

0: linear;

1: linear with averaging;

2: staircase;

3: staircase with averaging;

4: natural cubic spline;

5: natural cubic spline with averaging.

#### Note

The abscissae must be given in increasing order. If any of interpolation methods 1 ('linear with averaging'), 3 ('staircase with averaging'), and 5 ('natural cubic spline with averaging') is used, the number of returned values is one less than the number of targets and the targets values must be given in increasing order. Strings and empty cells in abscissae and ordinates are ignored. If several target data are provided they must be in the same column in consecutive cells.

#### See also

`PERIODOGRAM`.

`PERIODOGRAM`
`PERIODOGRAM` periodogram of the given data

    PERIODOGRAM(ordinates,filter,abscissae,interpolation,number)

#### Arguments

ordinates: ordinates of the given data

filter: windowing function to be used, defaults to no filter

abscissae: abscissae of the given data, defaults to regularly spaced abscissae

interpolation: method of interpolation, defaults to none

number: number of interpolated data points

#### Description

If an interpolation method is used, the number of returned values is one less than the number of targets and the targets values must be given in increasing order.

The output consists always of one column of numbers.

Possible interpolation methods are:

0: linear;

1: linear with averaging;

2: staircase;

3: staircase with averaging;

4: natural cubic spline;

5: natural cubic spline with averaging.

Possible window functions are:

0: no filter (rectangular window)

1: Bartlett (triangular window)

2: Hahn (cosine window)

3: Welch (parabolic window)

#### Note

Strings and empty cells in abscissae and ordinates are ignored. If several target data are provided they must be in the same column in consecutive cells.

#### See also

`INTERPOLATION`.